Question

which expression is equivalent to $\frac{2^{32}}{2^{-4}}$? $2^{-1}cdot2^{8}$ $\frac{1}{2^{-8}}$ $2^{-36}$ $(2^{6})^{6}$

Explanation:

Step1: Use exponent - division rule

According to the rule $\frac{a^m}{a^n}=a^{m - n}$, for $\frac{2^{32}}{2^{-4}}$, we have $2^{32-(-4)}$.

Step2: Simplify the exponent

$32-(-4)=32 + 4=36$, so $\frac{2^{32}}{2^{-4}}=2^{36}$.

Step3: Analyze each option

• For $2^{-1}\cdot2^{8}$, using the rule $a^m\cdot a^n=a^{m + n}$, we get $2^{-1 + 8}=2^{7}

eq2^{36}$.

• For $\frac{1}{2^{-8}}$, since $\frac{1}{a^{-n}}=a^{n}$, it is $2^{8}

eq2^{36}$.

• For $2^{-36}

eq2^{36}$.

• For $(2^{6})^{6}$, using the rule $(a^m)^n=a^{mn}$, we have $2^{6\times6}=2^{36}$.

Answer:

$(2^{6})^{6}$