which single power is equivalent to the expression $\frac{(4^{3})^{2}}{4^{2}}$? $4^{3}$ $4^{4}$ $4^{7}$…
which single power is equivalent to the expression $\frac{(4^{3})^{2}}{4^{2}}$? $4^{3}$ $4^{4}$ $4^{7}$ $4^{8}$
Answer
Explanation:
Step1: Simplify the numerator
Use the power - of - a - power rule $(a^m)^n=a^{mn}$. So, $(4^{3})^{2}=4^{3\times2}=4^{6}$.
Step2: Simplify the fraction
Use the rule $\frac{a^m}{a^n}=a^{m - n}$. Here, $a = 4$, $m = 6$, and $n = 2$. So, $\frac{4^{6}}{4^{2}}=4^{6 - 2}=4^{4}$.
Answer:
$4^{4}$