Gr 11 Math Ch 1 SUM: Exponents and Surds

What is the formula for exponential growth or decay?

P = P₀(1 + r)^t

What is the set of natural numbers represented by?

ℕ

What is the value of a^0 when a is not equal to 0?

1

What is the formula to find the nth root of a number?

a^(1/n) Signup and view all the answers

What is the set of real numbers represented by?

ℝ Signup and view all the answers

What is the formula to find the result of raising a number to a rational exponent?

(a^m)^(1/n) Signup and view all the answers

What is the definition of a rational number?

A number that can be written as a fraction with an integer in the numerator and the denominator Signup and view all the answers

What is the value of r in the equation r^n = a, where n ≥ 2?

r = a^(1/n) Signup and view all the answers

What is the value of a^(1/n)?

nth root of a Signup and view all the answers

What is the value of a^(-1/n)?

1 / a^(1/n) Signup and view all the answers

What is the purpose of rationalising the denominator?

To eliminate the surd from the denominator Signup and view all the answers

What is the product of powers law?

a^m × a^n = a^(m+n) Signup and view all the answers

What is the quotient of powers law?

a^m / a^n = a^(m-n) Signup and view all the answers

What is the value of √(a^m)?

a^(m/2) Signup and view all the answers

What is the power of a power rule in exponentiation?

(a^m)^n = a^(mn) Signup and view all the answers

What is the purpose of rationalizing denominators in surd expressions?

To eliminate radicals from the denominator Signup and view all the answers

What is the first step in solving surd equations?

Isolate the surd term by itself on one side of the equation Signup and view all the answers

What is the formula for exponential growth or decay?

P(t) = P_0 × (1 + r)^t Signup and view all the answers

What is the purpose of simplifying surd expressions?

To make the expression easier to work with Signup and view all the answers

What is the general rule for solving quadratic surd equations?

Isolate the surd, square both sides, and solve the quadratic equation Signup and view all the answers

What is the purpose of converting surds to exponential form?

To apply exponent rules and simplify the expression Signup and view all the answers

What is the key point to remember when solving surd equations?

Always check the solution by substituting back into the original equation Signup and view all the answers

What is the application of exponential growth and decay in finance?

Compound interest calculations Signup and view all the answers

What is the value of $a^{rac{m}{n}}$?

$\left(a^m ight)^{rac{1}{n}}$ Signup and view all the answers

What is the purpose of rationalizing the denominator in surd expressions?

To eliminate the surd from the denominator Signup and view all the answers

What is the value of $\sqrt[n]{a} imes \sqrt[n]{b}$?

$\sqrt[n]{ab}$ Signup and view all the answers

What is the value of $a^{-rac{1}{n}}$?

$rac{1}{\sqrt[n]{a}}$ Signup and view all the answers

What is the value of $\left(\sqrt[n]{a} ight)^m$?

$a^{rac{m}{n}}$ Signup and view all the answers

What is the initial step in solving exponential growth or decay problems?

Determine the initial amount, growth rate, and time period Signup and view all the answers

What is the condition for $r^n = a$ to have real roots?

$a > 0$ and $n \geq 2$ Signup and view all the answers

What is the value of $\sqrt[n]{a^m} imes \sqrt[n]{a^p}$?

$\sqrt[n]{a^{m+p}}$ Signup and view all the answers

Which set of numbers includes all rational and irrational numbers?

Real numbers Signup and view all the answers

What is the result of raising a number to a negative exponent?

The reciprocal of the number raised to the positive exponent Signup and view all the answers

What is the purpose of expressing surds in exponential form?

To make it easier to work with rational exponents Signup and view all the answers

What is the purpose of converting percentages to decimal form in exponential growth or decay problems?

To simplify the calculation Signup and view all the answers

What is the definition of $a^{rac{m}{n}}$?

The $n^{th}$ root of $a^m$ Signup and view all the answers

What is the result of applying the rules of exponents to the expression $(a^m)^n$?

The result is $a^{mn}$ Signup and view all the answers

What is the main goal when solving equations involving surds?

To eliminate the surd on one side of the equation Signup and view all the answers

What is the result of applying the power of a power rule to $(a^m)^n$?

$a^{mn}$ Signup and view all the answers

What is the purpose of rationalising the denominator in surd expressions?

To eliminate the surd from the denominator Signup and view all the answers

What is the formula for exponential decay?

$P(t) = P_0 imes (1 - r)^t$ Signup and view all the answers

What is the result of raising both sides of the equation to the power corresponding to the root when solving surd equations?

The surd is eliminated and the equation becomes quadratic Signup and view all the answers

What is the purpose of converting surds to exponential form?

To make the expression easier to manipulate Signup and view all the answers

What is the key point to remember when solving quadratic surd equations?

To check for extraneous solutions Signup and view all the answers

What is the application of exponential growth in finance?

To calculate the compound interest Signup and view all the answers

What is the result of applying the zero exponent rule to $a^0$?

$1$ Signup and view all the answers

What is the purpose of simplifying surd expressions?

To make the expression easier to manipulate Signup and view all the answers

What is the value of $a^{rac{m}{n}}$ in terms of radicals?

$\sqrt[n]{a^m}$ Signup and view all the answers

What is the purpose of rationalising the denominator in surd expressions?

To eliminate the surd from the denominator Signup and view all the answers

What is the value of $\sqrt[n]{a} imes \sqrt[n]{b}$?

$\sqrt[n]{ab}$ Signup and view all the answers

What is the value of $\left(\sqrt[n]{a} ight)^m$?

$a^{rac{m}{n}}$ Signup and view all the answers

What is the condition for $r^n = a$ to have real roots?

$a > 0$ and $n$ is any integer Signup and view all the answers

What is the purpose of simplifying surd expressions?

To express the radicand as a product of factors Signup and view all the answers

What is the value of $a^{-rac{1}{n}}$?

$rac{1}{\sqrt[n]{a}}$ Signup and view all the answers

What is the value of $\sqrt[n]{a} \div \sqrt[n]{b}$?

$\sqrt[n]{a/b}$ Signup and view all the answers

What is the first step in identifying the variables in an exponential growth or decay problem?

Determine the initial amount, growth rate, and time period Signup and view all the answers

What is the purpose of converting percentage rates to decimal form in exponential growth or decay problems?

To use the rates in the formula Signup and view all the answers

Which of the following sets of numbers includes all rational and irrational numbers?

Real numbers Signup and view all the answers

What is the result of applying the power of a power rule to the expression $(a^m)^n$?

$a^{mn}$ Signup and view all the answers

What is the value of $a^{rac{m}{n}}$ in terms of roots and powers?

$\sqrt[n]{a^m}$ Signup and view all the answers

What is the purpose of understanding the rules of exponents in solving exponential growth or decay problems?

To apply the formula correctly Signup and view all the answers

What is the purpose of converting surds to exponential form when solving surd equations?

To make manipulation easier Signup and view all the answers

What is the key point to remember when solving quadratic surd equations?

Always check for extraneous solutions Signup and view all the answers

What is the result of applying the power of a power rule to the expression $(a^m)^n$?

$a^{mn}$ Signup and view all the answers

What is the purpose of rationalising the denominator in surd expressions?

To make the expression easier to manipulate Signup and view all the answers

What is the main goal when solving equations involving surds?

To eliminate the surd Signup and view all the answers

What is the result of applying the rules of exponents to the expression $a^{rac{m}{n}}$?

$\sqrt[n]{a^m}$ Signup and view all the answers

What is the application of exponential growth in finance?

To calculate the compound interest Signup and view all the answers

What is the condition for $r^n = a$ to have real roots?

$a > 0$ Signup and view all the answers

What is the purpose of converting percentages to decimal form in exponential growth or decay problems?

To make the calculations easier Signup and view all the answers

What is the result of raising both sides of the equation to the power corresponding to the root when solving surd equations?

The surd is eliminated Signup and view all the answers

What is the value of $a^{frac{m}{n}}$ when $a > 0$ and $m, n ∈ ℤ$, $n ≠ 0$?

$\sqrt[n]{a^m}$ Signup and view all the answers

What is the purpose of rationalising the denominator in surd expressions?

To eliminate the surd from the denominator Signup and view all the answers

What is the value of $\sqrt[n]{a}$ when $a > 0$ and $n ∈ ℤ$, $n ≥ 2$?

$a^{frac{1}{n}}$ Signup and view all the answers

What is the result of applying the product of powers law to $a^m × a^n$?

$a^{m+n}$ Signup and view all the answers

What is the value of $\left(\sqrt[n]{a}\right)^m$ when $a > 0$ and $m, n ∈ ℤ$, $n ≠ 0$?

$a^{frac{m}{n}}$ Signup and view all the answers

What is the condition for $r^n = a$ to have real roots?

$a > 0$ and $n ∈ ℤ$, $n ≥ 2$ Signup and view all the answers

What is the value of $\sqrt[n]{a} × \sqrt[n]{b}$ when $a > 0$ and $b > 0$ and $n ∈ ℤ$, $n ≠ 0$?

$\sqrt[n]{ab}$ Signup and view all the answers

What is the purpose of simplifying surd expressions?

To express the radicand as a product of factors Signup and view all the answers

What is the correct way to convert a percentage rate into a decimal form?

Divide the percentage by 100 Signup and view all the answers

Which of the following sets of numbers includes all rational and irrational numbers?

\mathbb{R} Signup and view all the answers

What is the formula for the final amount in an exponential growth or decay problem?

P_0 (1 + r)^t Signup and view all the answers

What is the result of applying the power of a power rule to the expression (a^m)^n?

a^(mn) Signup and view all the answers

What is the value of a^(-1/n)?

1/a^(1/n) Signup and view all the answers

What is the formula to find the nth root of a number?

a^(1/n) Signup and view all the answers

What is the primary reason for converting surds to exponential form when solving surd equations?

To make it easier to apply the power of a power rule Signup and view all the answers

What is the key consideration when raising both sides of the equation to the power corresponding to the root when solving surd equations?

Avoiding the introduction of extraneous solutions Signup and view all the answers

What is the general approach to solving surd equations?

Isolate the surd term, eliminate the surd, and solve the resulting equation Signup and view all the answers

What is the purpose of factoring in solving quadratic surd equations?

To solve for the variable using the zero-product property Signup and view all the answers

What is the primary application of exponential growth and decay in finance?

Calculating compound interest Signup and view all the answers

What is the purpose of checking solutions when solving surd equations?

To verify that the solution is correct Signup and view all the answers

What is the general formula for exponential growth or decay?

P(t) = P_0 × (1 + r)^t Signup and view all the answers

What is the result of applying the power of a power rule to the expression (a^m)^n?

a^(mn) Signup and view all the answers

What is the key point to remember when solving quadratic surd equations?

Always check for extraneous solutions Signup and view all the answers

What is the primary application of exponential growth in finance?

Calculating the future value of a present amount Signup and view all the answers

What is the value of $a^{rac{m}{n}}$ in terms of radicals?

$\sqrt[n]{a^m}$ Signup and view all the answers

What is the purpose of rationalising the denominator in surd expressions?

To eliminate the surd from the denominator Signup and view all the answers

What is the result of applying the power of a power rule to $(a^m)^n$?

$a^{mn}$ Signup and view all the answers

What is the condition for $r^n = a$ to have real roots?

$r > 0, a > 0, n \geq 2$ Signup and view all the answers

What is the value of $\sqrt[n]{a^m} imes \sqrt[n]{a^p}$?

$\sqrt[n]{a^{m+p}}$ Signup and view all the answers

What is the result of applying the quotient of powers rule to $rac{a^m}{a^n}$?

$a^{m-n}$ Signup and view all the answers

If $x^{rac{1}{2}} = 4$, what is the value of $x^{rac{1}{4}}$?

2 Signup and view all the answers

Solve the equation $(2\sqrt{x})^2 = 32$:

x = 16 Signup and view all the answers

If $P(t) = 5000(1 + 0.05)^t$ represents the population growth of a city, what is the population after 5 years?

6617 Signup and view all the answers

Solve the equation $\sqrt{x} + 2 = 5$:

x = 9 Signup and view all the answers

What is the value of $(a^{rac{1}{2}})^4$ in terms of $a$?

a^4 Signup and view all the answers

Solve the equation $(3\sqrt{x})^2 = 48$:

x = 4 Signup and view all the answers

What is the initial amount in the exponential growth or decay formula?

P₀ Signup and view all the answers

Which of the following is a correct application of the power of a power rule?

(a^m)^n = a^(mn) Signup and view all the answers

What is the value of a^(-n) when a is not equal to 0?

1/a^n Signup and view all the answers

Which of the following sets of numbers includes all rational and irrational numbers?

R Signup and view all the answers

Gr 11 Math Ch 1 SUM: Exponents and Surds

Questions and Answers

What is the formula for exponential growth or decay?

What is the set of natural numbers represented by?

What is the value of a^0 when a is not equal to 0?

What is the formula to find the nth root of a number?

What is the set of real numbers represented by?

What is the formula to find the result of raising a number to a rational exponent?

What is the definition of a rational number?

What is the value of r in the equation r^n = a, where n ≥ 2?

What is the value of a^(1/n)?

What is the value of a^(-1/n)?

What is the purpose of rationalising the denominator?

What is the product of powers law?

What is the quotient of powers law?

What is the value of √(a^m)?

What is the power of a power rule in exponentiation?

What is the purpose of rationalizing denominators in surd expressions?

What is the first step in solving surd equations?

What is the formula for exponential growth or decay?

What is the purpose of simplifying surd expressions?

What is the general rule for solving quadratic surd equations?

What is the purpose of converting surds to exponential form?

What is the key point to remember when solving surd equations?

What is the application of exponential growth and decay in finance?

What is the value of $a^{rac{m}{n}}$?

What is the purpose of rationalizing the denominator in surd expressions?

What is the value of $\sqrt[n]{a} imes \sqrt[n]{b}$?

What is the value of $a^{-rac{1}{n}}$?

What is the value of $\left(\sqrt[n]{a} ight)^m$?

What is the initial step in solving exponential growth or decay problems?

What is the condition for $r^n = a$ to have real roots?

What is the value of $\sqrt[n]{a^m} imes \sqrt[n]{a^p}$?

Which set of numbers includes all rational and irrational numbers?

What is the result of raising a number to a negative exponent?

What is the purpose of expressing surds in exponential form?

What is the purpose of converting percentages to decimal form in exponential growth or decay problems?

What is the definition of $a^{rac{m}{n}}$?

What is the result of applying the rules of exponents to the expression $(a^m)^n$?

What is the main goal when solving equations involving surds?

What is the result of applying the power of a power rule to $(a^m)^n$?

What is the purpose of rationalising the denominator in surd expressions?

What is the formula for exponential decay?

What is the result of raising both sides of the equation to the power corresponding to the root when solving surd equations?

What is the purpose of converting surds to exponential form?

What is the key point to remember when solving quadratic surd equations?

What is the application of exponential growth in finance?

What is the result of applying the zero exponent rule to $a^0$?

What is the purpose of simplifying surd expressions?

What is the value of $a^{rac{m}{n}}$ in terms of radicals?

What is the purpose of rationalising the denominator in surd expressions?

What is the value of $\sqrt[n]{a} imes \sqrt[n]{b}$?

What is the value of $\left(\sqrt[n]{a} ight)^m$?

What is the condition for $r^n = a$ to have real roots?

What is the purpose of simplifying surd expressions?

What is the value of $a^{-rac{1}{n}}$?

What is the value of $\sqrt[n]{a} \div \sqrt[n]{b}$?

What is the first step in identifying the variables in an exponential growth or decay problem?

What is the purpose of converting percentage rates to decimal form in exponential growth or decay problems?

Which of the following sets of numbers includes all rational and irrational numbers?

What is the result of applying the power of a power rule to the expression $(a^m)^n$?

What is the value of $a^{rac{m}{n}}$ in terms of roots and powers?

What is the purpose of understanding the rules of exponents in solving exponential growth or decay problems?

What is the purpose of converting surds to exponential form when solving surd equations?

What is the key point to remember when solving quadratic surd equations?

What is the result of applying the power of a power rule to the expression $(a^m)^n$?

What is the purpose of rationalising the denominator in surd expressions?

What is the main goal when solving equations involving surds?

What is the result of applying the rules of exponents to the expression $a^{rac{m}{n}}$?

What is the application of exponential growth in finance?

What is the condition for $r^n = a$ to have real roots?

What is the purpose of converting percentages to decimal form in exponential growth or decay problems?

What is the result of raising both sides of the equation to the power corresponding to the root when solving surd equations?

What is the value of $a^{frac{m}{n}}$ when $a > 0$ and $m, n ∈ ℤ$, $n ≠ 0$?

What is the purpose of rationalising the denominator in surd expressions?

What is the value of $\sqrt[n]{a}$ when $a > 0$ and $n ∈ ℤ$, $n ≥ 2$?

What is the result of applying the product of powers law to $a^m × a^n$?

What is the value of $\left(\sqrt[n]{a}\right)^m$ when $a > 0$ and $m, n ∈ ℤ$, $n ≠ 0$?

What is the condition for $r^n = a$ to have real roots?

What is the value of $\sqrt[n]{a} × \sqrt[n]{b}$ when $a > 0$ and $b > 0$ and $n ∈ ℤ$, $n ≠ 0$?