select all the expressions that are equivalent to $(8^{-7})^{2}$. \n$8^{-14}$ \n$\frac{1}{8^{14}}$…

select all the expressions that are equivalent to $(8^{-7})^{2}$. \n$8^{-14}$ \n$\frac{1}{8^{14}}$ \n$\frac{1}{8^{-14}}$ \n$\frac{1}{8^{-5}}$ \nsubmit

select all the expressions that are equivalent to $(8^{-7})^{2}$. \n$8^{-14}$ \n$\frac{1}{8^{14}}$ \n$\frac{1}{8^{-14}}$ \n$\frac{1}{8^{-5}}$ \nsubmit

Answer

Explanation:

Step1: Apply exponent power rule

When raising a power to a power, multiply exponents: $(a^m)^n = a^{m \times n}$. For $(8^{-7})^2$, calculate $-7 \times 2 = -14$, so $(8^{-7})^2 = 8^{-14}$.

Step2: Rewrite negative exponent

A negative exponent means the reciprocal: $a^{-k} = \frac{1}{a^k}$. For $8^{-14}$, this becomes $\frac{1}{8^{14}}$.

Step3: Eliminate incorrect options

  • $\frac{1}{8^{-14}} = 8^{14}$, which is not equal to $8^{-14}$.
  • $\frac{1}{8^{-5}} = 8^{5}$, which is not equal to $8^{-14}$.

Answer:

$8^{-14}$, $\frac{1}{8^{14}}$