Bot GPT 4-o mini 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:
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(−5)0: This represents a number raised to the power of zero, which equals 1, but does not involve a Power Rule application.
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(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: \( 7^{4 \cdot 8} \).
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129: This is just a number raised to a power and does not involve applying the Power Rule.
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(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.
1 answer