Question
Power Rule of Exponents Quick Check
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
Answers
GPT-4o mini
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)**.
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)**.