Which of the following correctly used the Power Rule of Exponents in the expression (109)7?(1 point)
Responses
1016
10 superscript 16 baseline
102
10 superscript 2 baseline
907
90 superscript 7 baseline
1063
10^63
Use the Power Rule of Exponents to create an expression equivalent to (156)2 .(1 point)
Responses
154
15 superscript 4 baseline
153
15 cubed
158
15 superscript 8 baseline
1512
15^12
What exponent would make the two expressions equivalent: (33)x=324 ?(1 point)
Responses
15
15
21
21
27
27
8
The exponent that would make the two expressions equivalent is 2 (27).
The correct response that uses the Power Rule of Exponents in the expression (109)7 is:
(10^9)^7
To simplify this expression, we apply the Power Rule of Exponents, which states that when raising a power to another power, we multiply the exponents:
(10^9)^7 = 10^(9 * 7)
Therefore, the correct answer is 10^63.
To correctly apply the Power Rule of Exponents to the expression (109)7, we need to raise the base (109) to the power of 7. The Power Rule states that when you have a base raised to an exponent, and that whole power is raised to another exponent, you can multiply the exponents.
In this case, we have (109)7, so we need to multiply the exponents. The exponent of the base 109 is 7, and the exponent of the entire expression (109) is 1. Multiplying these exponents gives us 7 * 1 = 7.
Therefore, the correct answer is 907, as 109 raised to the power of 7 is equal to 907.