To determine which expression is correctly developed to use the Power Rule of Exponents, we need to assess each option based on the Power Rule, which states that \( (a^m)^n = a^{m \cdot n} \).
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(7 to the fourth power) to the eighth power:
- This can be expressed as \( (7^4)^8 = 7^{4 \cdot 8} = 7^{32} \).
- This expression correctly applies the Power Rule.
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12 to the ninth power:
- This is simply \( 12^9 \).
- This doesn't invoke the Power Rule as it stands as a single exponent without further manipulation.
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(7 to the eighth power) times (7 to the tenth power):
- This can be simplified using the Product Rule of Exponents, which states that \( a^m \cdot a^n = a^{m+n} \).
- So, it becomes \( 7^8 \cdot 7^{10} = 7^{8 + 10} = 7^{18} \).
- This option uses the Product Rule, not the Power Rule.
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(-5) to the zero power:
- According to the Zero Exponent Rule, any non-zero number raised to the zero power is 1: \( (-5)^0 = 1 \).
- This expression does not include the Power Rule.
Based on this analysis, option 1 is the correctly developed expression that uses the Power Rule of Exponents.
5 answers