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Select all the expressions that are equivalent to $5^{-9} \times 5^{9}$ . $\newline$ Multi-select Choices: $\newline$ (A) $5^{0}$ $\newline$ (B) $5^{-81}$ $\newline$ (C) $1$ $\newline$ (D) $\frac{1}{5^{0}}$

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Simplify exponential expressions using exponent rules

Full solution

Q. Select all the expressions that are equivalent to

5^{-9} \times 5^{9}

.

\newline

Multi-select Choices:

\newline

(A)

5^{0}

\newline

(B)

5^{-81}

\newline

(C)

1

\newline

(D)

\frac{1}{5^{0}}

Simplify Expression: Simplify the expression $5^{-9} \times 5^{9}$ . $\newline$ When multiplying powers with the same base, we add the exponents. $\newline$ $5^{-9} \times 5^{9} = 5^{(-9 + 9)} = 5^{0}$
Find Value: Determine the value of $5^0$ . $\newline$ Any non-zero number raised to the power of $0$ is $1$ . $\newline$ $5^0 = 1$
Check Choices: Check the multi-select choices against the simplified expression. $\newline$ (A) $5^0$ is equivalent to our simplified expression, which is $1$ . $\newline$ (B) $5^{-81}$ is not equivalent because the exponents do not add up to $0$ . $\newline$ (C) $1$ is equivalent to our simplified expression, which is $5^0$ . $\newline$ (D) $1/5^0$ is equivalent to $1$ because $5^0$ is $1$ and $1$ divided by $1$ is $1$ .

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