Powers and Exponents in Pre-Algebra Quiz

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Questions and Answers

What is the result of $2^4 \cdot 2^3$?

$2^1$

$2^{43}$

$2^{12}$

$2^7$ (correct)

What is the value of $5^{-2}$?

$\frac{1}{25}$ (correct)

$-25$

$25$

$-1$

If $3^5 \div 3^2 = 3^n$, what is the value of $n$?

$7$

$10$

$-1$

$3$ (correct)

What is the result of $5^0$?

1 Signup and view all the answers

What is the simplified form of $25^3/5^3$?

$(25/5)^3$ Signup and view all the answers

What is the mass of the Sun expressed in scientific notation?

$1.989 \times 10^{30}$ kilograms Signup and view all the answers

What is the age of the Earth in years expressed in scientific notation?

$4.55 \times 10^9$ years Signup and view all the answers

What is the exponent in the expression $5^3$?

3 Signup and view all the answers

According to the multiplication law of exponents, what is the product of $2^4$ and $2^6$?

$2^{10}$ Signup and view all the answers

What happens when a base with a negative power is raised to a negative exponent?

It results in a reciprocal with a positive power Signup and view all the answers

What is the result of $2^3 \cdot 2^4$?

$2^7$ Signup and view all the answers

What is the simplified form of $10^6 \div 10^3$?

$10^3$ Signup and view all the answers

What is the value of $(-2)^{-4}$?

$-\frac{1}{16}$ Signup and view all the answers

What is the main difference between power and exponent?

Exponent is a small number placed above and to the right of the base number, while power consists of the base number and the exponent. Signup and view all the answers

What does 5^2.53 equal to?

$5^{2.53} = 5^2 imes 5^{0.53}$ Signup and view all the answers

Express the expression $10 imes 10 imes 10$ in exponent form.

$10 imes 10 imes 10 = 10^3$ Signup and view all the answers

What is the result of $5^5 / 5^2$?

$5^5 / 5^2 = 5^{5-2}$ Signup and view all the answers

What is the result of $2^8 imes 2^{-3}$?

$2^5$ Signup and view all the answers

What is the simplified form of $7^4 imes 7^{-2} imes 7^3$?

$7^9$ Signup and view all the answers

If $5^{2x} = 25$, what is the value of $x$?

$1/2$ Signup and view all the answers

What is the result of $2^4 \div 2^6$?

$2^{-2}$ Signup and view all the answers

If $(-3)^{-2}$ is expressed without negative exponents, what is the result?

$\frac{1}{9}$ Signup and view all the answers

Which law of exponents states that the product of two exponents with the same base and different powers equals the base raised to the sum of the two powers?

Multiplication law Signup and view all the answers

What is the result of $2^4 \cdot 2^3$?

$2^7$ Signup and view all the answers

If $3^{5x} = 81$, what is the value of $x$?

$x = \frac{1}{5}$ Signup and view all the answers

What is the simplified form of $10^6 \div 10^3$?

$10^3$ Signup and view all the answers

What is the result of $2^{10} imes 2^7$?

$2^{17}$ Signup and view all the answers

If $3^{2x} = 81$, what is the value of $x$?

3 Signup and view all the answers

What is the result of $4^5 imes 2^5$?

$16^{5}$ Signup and view all the answers

What is the simplified form of $(6^3)^4$?

$6^{12}$ Signup and view all the answers

Study Notes

Exponents and Powers: Key Concepts and Rules

Exponents and powers are used to represent large or small numbers in a simplified manner
3 x 3 x 3 x 3 can be written as 3^4, where 4 is the exponent and 3 is the base
An exponent represents the number of times a number is multiplied to itself
The exponentiation is the shorthand method of repeated multiplication
The laws of exponents are based on the powers they carry
The multiplication law states that the product of two exponents with the same base and different powers equals the base raised to the sum of the two powers
The division law states that when two exponents with the same base and different powers are divided, the result is the base raised to the difference between the two powers
The negative exponent law states that any base with a negative power results in a reciprocal with a positive power
The exponent is a small number positioned at the up-right of the base number
Powers and exponents are used to denote large numbers as powers of 10
Exponents are also called powers or indices
The exponent of a number represents the number of times the number is multiplied to itself

Exponents and Powers: Key Concepts and Rules

Exponents and powers are used to represent large or small numbers in a simplified manner.
An exponent represents the number of times a number is multiplied to itself.
The general form of exponents is expressed as a^n, where 'a' is the base and 'n' is the exponent.
The laws of exponents include the multiplication law, division law, and negative exponent law.
Rules for exponents include the property of zero, power of a power, power of a product, and power of a quotient.
The solved examples demonstrate the application of these rules and concepts.
Scientific notation uses exponents to express very large or small numbers in a compact form.
The distance between the Sun and the Earth, the mass of the Sun, and the age of the Earth can be expressed using exponents and powers.
Video lessons cover important concepts related to powers and exponents.
The difference between power and exponent is that power denotes repeated multiplication of a factor, while the number raised to that base factor is the exponent.

Exponents and Powers: Key Concepts and Rules

Exponents and powers are used to represent large or small numbers in a simplified manner
3 x 3 x 3 x 3 can be written as 3^4, where 4 is the exponent and 3 is the base
An exponent represents the number of times a number is multiplied to itself
The exponentiation is the shorthand method of repeated multiplication
The laws of exponents are based on the powers they carry
The multiplication law states that the product of two exponents with the same base and different powers equals the base raised to the sum of the two powers
The division law states that when two exponents with the same base and different powers are divided, the result is the base raised to the difference between the two powers
The negative exponent law states that any base with a negative power results in a reciprocal with a positive power
The exponent is a small number positioned at the up-right of the base number
Powers and exponents are used to denote large numbers as powers of 10
Exponents are also called powers or indices
The exponent of a number represents the number of times the number is multiplied to itself

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Description

Test your understanding of powers and exponents in pre-algebra with this quiz. Explore how to calculate expressions using exponents and understand the concepts of base and exponent.