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:
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\((-5)^0\) - This is a valid expression, and according to the zero exponent rule, this equals 1 but does not invoke the power rule.
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\(12^9\) - This does not involve another exponent applied to it, so no power rule is applied here.
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\( (7^8) \cdot (7^{10}) \) - This expression can be simplified using the Product of Powers Rule (which states that when multiplying with the same base, you add the exponents).
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\( (7^4)^8 \) - 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).
1 answer