Question

Which expression is correctly developed to use the Power Rule of Exponents?(1 point)
Responses

(78)⋅(710)
left parenthesis 7 superscript 8 baseline right parenthesis times left parenthesis 7 superscript 10 baseline right parenthesis

(74)8
left parenthesis 7 superscript 4 baseline right parenthesis superscript 8 baseline

129
12 superscript 9 baseline

(−5)0

Answer 1

The expression that is correctly developed to use the Power Rule of Exponents is:

\((7^8) \cdot (7^{10})\)

This expression can be simplified using the Power Rule of Exponents which states that when you multiply like bases, you add the exponents:

\[
7^8 \cdot 7^{10} = 7^{8+10} = 7^{18}
\]

The other options do not represent a correct application of the Power Rule for exponents:

- \((7^4)^8\) would involve the Power of a Power rule, which states that \((a^m)^n = a^{m \cdot n}\) but is not relevant here.
- \(12^9\) is just a single number raised to a power and doesn't involve the Power Rule of Exponents.
- \((-5)^0\) equals 1 due to the zero exponent rule, but also doesn't apply the Power Rule directly in a way that involves combining exponents.

Therefore, the first response is the most suitable for the Power Rule of Exponents.