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Select all the expressions that are equivalent to $5^{-5} \times 5^{-5}$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{5^{25}}$ $\newline$ (B) $5^{25}$ $\newline$ (C) $\frac{1}{5^{-10}}$ $\newline$ (D) $\frac{1}{5^{10}}$

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Simplify exponential expressions using exponent rules

Full solution

Q. Select all the expressions that are equivalent to

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

.

\newline

Multi-select Choices:

\newline

(A)

\frac{1}{5^{25}}

\newline

(B)

5^{25}

\newline

(C)

\frac{1}{5^{-10}}

\newline

(D)

\frac{1}{5^{10}}

Simplify Expression: Simplify the expression $5^{-5} \times 5^{-5}$ . We need to add the exponents because the bases are the same. $5^{-5} \times 5^{-5} = 5^{(-5 + -5)} = 5^{-10}$
Convert to Fractional Form: Convert $5^{-10}$ to a fractional form. $\newline$ $5^{-10}$ means $1$ divided by $5^{10}$ . $\newline$ So, $5^{-10} = \frac{1}{5^{10}}$
Compare to Choices: Compare the simplified expression to the choices. $\newline$ $\frac{1}{5^{10}}$ matches choice (D). $\newline$ Check other choices: $\newline$ (A) $\frac{1}{5^{25}}$ is not equal to $\frac{1}{5^{10}}$ . $\newline$ (B) $5^{25}$ is the reciprocal of $\frac{1}{5^{25}}$ , not $\frac{1}{5^{10}}$ . $\newline$ (C) $\frac{1}{5^{-10}}$ is actually $5^{10}$ , which is not $\frac{1}{5^{10}}$ .

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