which expressions are equivalent to $(2^{5})^{-2}$?\n$2^{-10}$ and $\frac{1}{20}$\n$2^{-10}$ and…

which expressions are equivalent to $(2^{5})^{-2}$?\n$2^{-10}$ and $\frac{1}{20}$\n$2^{-10}$ and $\frac{1}{1024}$\n$10^{-2}$ and $\frac{1}{100}$\n$10^{-10}$ and $\frac{1}{100}$

which expressions are equivalent to $(2^{5})^{-2}$?\n$2^{-10}$ and $\frac{1}{20}$\n$2^{-10}$ and $\frac{1}{1024}$\n$10^{-2}$ and $\frac{1}{100}$\n$10^{-10}$ and $\frac{1}{100}$

Answer

Explanation:

Step1: Apply power - of - a - power rule

According to the rule $(a^m)^n=a^{m\times n}$. For $(2^5)^{-2}$, we have $m = 5$ and $n=-2$, so $(2^5)^{-2}=2^{5\times(-2)}=2^{- 10}$.

Step2: Calculate the value of $2^{-10}$

We know that $a^{-n}=\frac{1}{a^n}$. So $2^{-10}=\frac{1}{2^{10}}$, and $2^{10}=1024$, then $2^{-10}=\frac{1}{1024}$.

Answer:

$2^{-10}$ and $\frac{1}{1024}$