Question

which expression is equivalent to 6·6^{-4}?
\frac{1}{6^{3}}
\frac{1}{6^{-4}}
\frac{1}{6^{-3}}
6^{-4}

Explanation:

Step1: Use exponent - product rule

According to the rule $a^m\times a^n=a^{m + n}$, for $6\times6^{-4}$, where $a = 6$, $m = 1$ and $n=-4$, we have $6^1\times6^{-4}=6^{1+( - 4)}$.

Step2: Calculate the exponent

$6^{1+( - 4)}=6^{1 - 4}=6^{-3}$.

Step3: Use negative - exponent rule

The negative - exponent rule is $a^{-n}=\frac{1}{a^n}$. So, $6^{-3}=\frac{1}{6^3}$.

Answer:

$\frac{1}{6^3}$