What is the missing number in this simplified exponential expression: 7?÷75=712?(1 point)
The missing number in this simplified exponential expression should be a 2 because 7^2 ÷ 75 = 7^12.
Use the Power Rule of Exponents to simplify (103)6.
The Power Rule of Exponents states that when a base is raised to an exponent and that is then raised to another exponent, we can multiply the exponents.
Therefore, in order to simplify (103)^6, we need to multiply the exponent of 3 by 6.
3 * 6 = 18
So (103)^6 simplifies to 10^18.
If the expression 715 was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression?
If the expression 715 was simplified using the Power Rule of Exponents, an expanded equivalent expression would be 7^1 * 15^1, since the number 715 can be split into its prime factors: 7 and 5.
If the expression 715 was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression?(1 point)
Responses
(710)5
left parenthesis 7 superscript 10 baseline right parenthesis superscript 5 baseline
(718)3
left parenthesis 7 superscript 18 baseline right parenthesis cubed
(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)
left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis
(7⋅7⋅7⋅7⋅7)10
If the expression 715 was simplified using the Power Rule of Exponents, the correct expanded equivalent expression would be:
(7 ⋅ 5) ⋅ (7 ⋅ 5) ⋅ (7 ⋅ 5)
This can also be written as:
7^3 ⋅ 5^3
Use the Power Rule of Exponents to create a simplified equivalent expression for (194)9.
To create a simplified equivalent expression for (194)^9 using the Power Rule of Exponents, we need to apply the rule that states that when a base is raised to an exponent and that expression is then raised to another exponent, we can multiply the exponents.
In this case, we have (194)^9, and since the base 194 has an exponent of 1, we can rewrite it as (1^9)(9^9)(4^9).
Simplifying further, we have:
1^9 = 1
9^9 = 9^9
4^9 = 4^9
Therefore, a simplified equivalent expression for (194)^9 is 1 * 9^9 * 4^9.