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

Question

Responses

a. (−5) to the power of 0
left parenthesis negative 5 right parenthesis superscript 0 baseline

b. (7 to the power of 8)⋅(7 to the power of 10)
left parenthesis 7 superscript 8 baseline right parenthesis times left parenthesis 7 superscript 10 baseline right parenthesis

c. (7 to the power of 4) to the power of 8
left parenthesis 7 superscript 4 baseline right parenthesis superscript 8 baseline

d. 12 to the power of 9

Answer 1

The Power Rule of Exponents states that when you raise a power to another power, you multiply the exponents. This is represented as \((a^m)^n = a^{m \cdot n}\).

Among the given options, option c \((7^4)^8\) is the only expression that can be correctly developed using the Power Rule:

\[ (7^4)^8 = 7^{4 \cdot 8} = 7^{32} \]

The other options do not involve raising a power to another power:

• a. \((-5)^0\) is equal to 1, following the zero exponent rule but does not apply the Power Rule.
• b. \((7^8) \cdot (7^{10})\) would apply the Product of Powers rule, resulting in \(7^{8 + 10} = 7^{18}\) instead.
• d. \(12^9\) is just a base raised to a power with no application of the Power Rule.

So, the correct answer is c.