Question

9 which expression is equivalent to $8^{4} \cdot 8^{-10}$? \\(\boldsymbol{\text{a}}\\) \\(\frac{1}{8^{6}}\\) \\(\boldsymbol{\text{b}}\\) \\(\frac{1}{8^{14}}\\) \\(\boldsymbol{\text{c}}\\) \\(\frac{1}{8^{40}}\\)

Explanation:

Step1: Use the exponent rule \(a^m \cdot a^n = a^{m + n}\)

For \(8^4 \cdot 8^{-10}\), we add the exponents: \(4+(-10)=4 - 10=-6\), so \(8^4 \cdot 8^{-10}=8^{-6}\)

Step2: Use the rule \(a^{-n}=\frac{1}{a^n}\)

For \(8^{-6}\), applying the rule, we get \(\frac{1}{8^6}\)

Answer:

A. \(\frac{1}{8^6}\)