Power Rule of Exponents Quick Check

Question

2 of 52 of 5 Items
Question
Which of the following correctly used the Power Rule of Exponents in the expression (10^9)^7?(1 point)
Responses

10^63
10 superscript 63 baseline

90^7
90 superscript 7 baseline

10^2
10 superscript 2 baseline

10^16

Answer 1

To apply the Power Rule of Exponents, you multiply the exponents when raising a power to another power. The Power Rule states that \((a^m)^n = a^{m \cdot n}\).

In the expression \((10^9)^7\):

1. \(a = 10\)
2. \(m = 9\)
3. \(n = 7\)

Using the Power Rule:

\[ (10^9)^7 = 10^{9 \cdot 7} = 10^{63} \]

Therefore, the correct response that used the Power Rule of Exponents correctly in the expression \((10^9)^7\) is:

10^63 (10 superscript 63 baseline).