30 Questions
What is the result of $2^4 \cdot 2^3$?
$2^7$
What is the value of $5^{-2}$?
$\frac{1}{25}$
If $3^5 \div 3^2 = 3^n$, what is the value of $n$?
$3$
What is the result of $5^0$?
1
What is the simplified form of $25^3/5^3$?
$(25/5)^3$
What is the mass of the Sun expressed in scientific notation?
$1.989 \times 10^{30}$ kilograms
What is the age of the Earth in years expressed in scientific notation?
$4.55 \times 10^9$ years
What is the exponent in the expression $5^3$?
3
According to the multiplication law of exponents, what is the product of $2^4$ and $2^6$?
$2^{10}$
What happens when a base with a negative power is raised to a negative exponent?
It results in a reciprocal with a positive power
What is the result of $2^3 \cdot 2^4$?
$2^7$
What is the simplified form of $10^6 \div 10^3$?
$10^3$
What is the value of $(-2)^{-4}$?
$-\frac{1}{16}$
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.
What does 5^2.53 equal to?
$5^{2.53} = 5^2 imes 5^{0.53}$
Express the expression $10 imes 10 imes 10$ in exponent form.
$10 imes 10 imes 10 = 10^3$
What is the result of $5^5 / 5^2$?
$5^5 / 5^2 = 5^{5-2}$
What is the result of $2^8 imes 2^{-3}$?
$2^5$
What is the simplified form of $7^4 imes 7^{-2} imes 7^3$?
$7^9$
If $5^{2x} = 25$, what is the value of $x$?
$1/2$
What is the result of $2^4 \div 2^6$?
$2^{-2}$
If $(-3)^{-2}$ is expressed without negative exponents, what is the result?
$\frac{1}{9}$
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
What is the result of $2^4 \cdot 2^3$?
$2^7$
If $3^{5x} = 81$, what is the value of $x$?
$x = \frac{1}{5}$
What is the simplified form of $10^6 \div 10^3$?
$10^3$
What is the result of $2^{10} imes 2^7$?
$2^{17}$
If $3^{2x} = 81$, what is the value of $x$?
3
What is the result of $4^5 imes 2^5$?
$16^{5}$
What is the simplified form of $(6^3)^4$?
$6^{12}$
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
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.
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