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 129 12 superscript 9 baseline (78)⋅(710) left parenthesis 7 superscript 8 baseline right parenthesis times left parenthesis 7 superscript 10 baseline right parenthesis (74)8

Answer 1

The Power Rule of Exponents states that when you raise a power to another power, you multiply the exponents. In order to correctly develop an expression to use this rule, we need to focus on mathematical expressions that involve exponents with a base raised to a power.

Among the options you've provided:

1. \((-5)^0\) - This is a valid expression, and according to the zero exponent rule, this equals 1 but does not invoke the power rule.

2. \(12^9\) - This does not involve another exponent applied to it, so no power rule is applied here.

3. \( (7^8) \cdot (7^{10}) \) - This expression can be simplified using the Product of Powers Rule (which states that when multiplying with the same base, you add the exponents).

4. \( (7^4)^8 \) - This expression can be simplified using the Power of a Power Rule (which is what you're asking for). Here, you would multiply the exponents (4 and 8), leading to \( 7^{32} \).

Out of these expressions, the correct one for applying the Power Rule is:

**(7^4)^8**

This can be developed to use the Power Rule of Exponents by multiplying the exponents (4 and 8).