select all the expressions that are equivalent to $(8^{5})^{-2}$. \n$8^{-10}$ \n$\frac{1}{8^{-10}}$…
select all the expressions that are equivalent to $(8^{5})^{-2}$. \n$8^{-10}$ \n$\frac{1}{8^{-10}}$ \n$\frac{1}{8^{10}}$ \n$\frac{1}{8^{3}}$ \nsubmit
Answer
Explanation:
Step1: Apply exponent power rule
$(a^m)^n = a^{m \times n}$ So, $(8^5)^{-2} = 8^{5 \times (-2)} = 8^{-10}$
Step2: Apply negative exponent rule
$a^{-n} = \frac{1}{a^n}$ So, $8^{-10} = \frac{1}{8^{10}}$
Step3: Verify other options
$\frac{1}{8^{-10}} = 8^{10}$, which is not equivalent. $\frac{1}{8^3}=8^{-3}$, which is not equivalent.
Answer:
$8^{-10}$, $\frac{1}{8^{10}}$