Question

which expression is equivalent to $\frac{11^{31}}{11^{-1}}$? $\frac{1}{11^{-32}}$ $\frac{1}{11^{-31}}$ $11^{30}$ $11^{-32}$

Explanation:

Step1: Apply exponent - division rule

Use the rule $\frac{a^m}{a^n}=a^{m - n}$. Here, $a = 11$, $m = 31$, and $n=-1$. So, $\frac{11^{31}}{11^{-1}}=11^{31-(-1)}$.

Step2: Simplify the exponent

$31-(-1)=31 + 1=32$. So, $11^{31-(-1)}=11^{32}$. Also, $\frac{1}{11^{-32}}=11^{32}$ (since $\frac{1}{a^{-n}}=a^{n}$).

Answer:

$\frac{1}{11^{-32}}$