Which of the following correctly used the Power Rule of Exponents in the expression (10^9)^7?(1 point)
Responses
90^7
90 superscript 7 baseline
10^63
10 superscript 63 baseline
10^2
10 superscript 2 baseline
10^16
10^63
If the expression 4^10 was simplified using the Power Rule of Exponents, what is an equivalent expanded expression? (1 point)
Responses
(4^12)^2
left parenthesis 4 superscript 12 baseline right parenthesis squared
(4^2)^8
left parenthesis 4 squared right parenthesis superscript 8 baseline
(4^5)^2
left parenthesis 4 superscript 5 baseline right parenthesis squared
4⋅4⋅4⋅4⋅4⋅4⋅4
(4^5)^2
Use the Power Rule of Exponents to create an expression equivalent to (15^6)^2.(1 point)
Responses
15^8
15 superscript 8 baseline
15^4
15 superscript 4 baseline
15^3
15 cubed
15^12
15^12
What exponent would make the two expressions equivalent: (3^3^)x=3^24?(1 point)
Responses
27
27
15
15
8
8
21
8
are all of these answers right?
No, only one of the answers is correct. The correct exponent that would make the two expressions equivalent is 8.
To correctly use the Power Rule of Exponents in the expression (10^9)^7, we need to raise the base (10^9) to the power of the exponent (7). The Power Rule states that when raising an exponent to another exponent, we need to multiply the exponents together.
Therefore, to find the correct answer, we need to multiply 9 (the exponent of the base) by 7 (the exponent of the entire expression).
10^9 * 7 = 10^63.
So, the correct response is: 10^63.