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Select all the expressions that are equivalent to $(8^{-9})^0$ . $\newline$ Multi-select Choices: $\newline$ (A) $8^{-9}$ $\newline$ (B) $\frac{1}{8^{-9}}$ $\newline$ (C) $\frac{1}{8^0}$ $\newline$ (D) $8$

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Simplify exponential expressions using exponent rules

Full solution

Q. Select all the expressions that are equivalent to

(8^{-9})^0

.

\newline

Multi-select Choices:

\newline

(A)

8^{-9}

\newline

(B)

\frac{1}{8^{-9}}

\newline

(C)

\frac{1}{8^0}

\newline

(D)

8

Simplify Power: Step $1$ : Simplify $(8^{-9})^0$ . $\newline$ Any number raised to the power of zero is $1$ . $\newline$ $(8^{-9})^0 = 1$
Compare with $8^{-9}$ : Step $2$ : Compare with choice (A) $8^{-9}$ . $8^{-9}$ is not equal to $1$ ; it's a very small fraction. $8^{-9} \neq 1$
Compare with $1/8^{-9}$ : Step $3$ : Compare with choice $(B)$ $1/8^{-9}$ . $1/8^{-9}$ simplifies to $8^9$ , which is a very large number. $1/8^{-9} \neq 1$
Compare with $1/8^0$ : Step $4$ : Compare with choice (C) $1/8^0$ . $\newline$ Since any number to the power of zero is $1$ , $1/8^0$ simplifies to $1/1$ , which is $1$ . $\newline$ $1/8^0 = 1$
Compare with $8$ : Step $5$ : Compare with choice (D) $8$ . $\newline$ $8$ is clearly not equal to $1$ . $\newline$ $8 \neq 1$

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