Question

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

(−5)0
left parenthesis negative 5 right parenthesis superscript 0 baseline

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

129
12 superscript 9 baseline

(78)⋅(710)
left parenthesis 7 superscript 8 baseline right parenthesis times left parenthesis 7 superscript 10 baseline right parenthesis
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Answer 1

To correctly apply the Power Rule of Exponents, we need to be looking for expressions that involve raising a power to another power, multiplying powers with the same base, or simplifying any other form of exponentiation.

Let's analyze the provided options:

1. **(−5)0**: This represents a number raised to the power of zero, which equals 1, but does not involve a Power Rule application.

2. **(74)8**: This represents raising a power (7 raised to the 4th power) to another power (8). According to the Power Rule, \( (a^m)^n = a^{m \cdot n} \), this can be simplified by multiplying the exponents: \( 7^{4 \cdot 8} \).

3. **129**: This is just a number raised to a power and does not involve applying the Power Rule.

4. **(78)⋅(710)**: This involves multiplying two powers with the same base. According to the Power Rule, \( a^m \cdot a^n = a^{m+n} \). Here, you can add the exponents: \( 7^{8+10} \).

Based on the analysis, both **(74)8** and **(78)⋅(710)** correctly involve applications of the Power Rule of Exponents. However, since the prompt asks for one expression to be correctly developed, **(74)8** is a more explicit application of the Power Rule where you are raising a power to another power.

Thus, the best answer is:
**(74)8**.