Frazier Hilton
07/25/2024 · Middle School
Which expression is correctly developed to use the Power Rule of Exponents? (1 point) \( (-5)^{0} \) \( \left(7^{4}\right)^{8} \) \( 12^{9} \) \( \left(7^{8}\right) \cdot\left(7^{10}\right) \)
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Step-by-step Solution
The Power Rule of Exponents states that \( (a^m)^n = a^{m \cdot n} \) and \( a^m \cdot a^n = a^{m+n} \).
Let's analyze each expression:
1. \( (-5)^{0} \): This expression equals 1, but it does not involve the Power Rule.
2. \( \left(7^{4}\right)^{8} \): This can be developed using the Power Rule: \( (7^4)^8 = 7^{4 \cdot 8} = 7^{32} \).
3. \( 12^{9} \): This is a single exponent and does not involve the Power Rule.
4. \( \left(7^{8}\right) \cdot\left(7^{10}\right) \): This can also be developed using the Power Rule: \( 7^8 \cdot 7^{10} = 7^{8+10} = 7^{18} \).
The expressions that can be developed using the Power Rule are \( \left(7^{4}\right)^{8} \) and \( \left(7^{8}\right) \cdot\left(7^{10}\right) \). However, since the question asks for which expression is correctly developed to use the Power Rule, the best answer is:
**\( \left(7^{4}\right)^{8} \)**.
Quick Answer
The expression correctly developed to use the Power Rule is \( \left(7^{4}\right)^{8} \).
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