Select all the expressions that are equivalent to (8^-9)^0. Multi-select Choices: (A)8^-9 (B)1/8^-9 (C)1/8^0 (D)8

Simplify Power: Step 1: Simplify (8^-9)^0. Any number raised to the power of zero is 1. (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 ≠ 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 ≠ 1 Compare with 1/8^0: Step 4: Compare with choice (C) 1/8^0. Since any number to the power of zero is 1, 1/8^0 simplifies to 1/1, which is 1. 1/8^0 = 1 Compare with 8: Step 5: Compare with choice (D) 8. 8 is clearly not equal to 1. 8 ≠ 1

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Math Problems

Algebra 1

Simplify exponential expressions using exponent rules

Full solution

Q. Select all the expressions that are equivalent to

(8^{-9})^0

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Multi-select Choices:

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(A)

8^{-9}

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(B)

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

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(C)

\frac{1}{8^0}

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(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 $1$ . $\newline$ $8 \neq 1$