Question

Which expression is correctly developed to use the Power Rule of Exponents? Responses 12^9 (7^4)^8 (−5)^0 (7^8)⋅(7^10)

Answer 1

The Power Rule of Exponents states that \((a^m)^n = a^{m \cdot n}\). We can apply this rule to the expression \((7^4)^8\).

Let's break down each option:

1. **\(12^9\)**: This expression is already in its simplest form and does not require the Power Rule of Exponents.

2. **\((7^4)^8\)**: This expression can be evaluated using the Power Rule:
\[
(7^4)^8 = 7^{4 \cdot 8} = 7^{32}
\]
Thus, this is correctly developed using the Power Rule.

3. **\((-5)^0\)**: According to the property of exponents, any non-zero number raised to the power of 0 equals 1. Hence, this expression does not involve the Power Rule.

4. **\((7^8) \cdot (7^{10})\)**: This expression can be simplified using the rule \(a^m \cdot a^n = a^{m+n}\), but it is not an application of the Power Rule of Exponents.

Therefore, the correct expression that uses the Power Rule of Exponents is **\((7^4)^8\)**.