Select all the expressions that are equivalent to 5^-5 * 5^-5. Multi-select Choices: (A)1/5^25 (B)5^25 (C)1/5^-10 (D)1/5^10

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

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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

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

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Multi-select Choices:

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(A)

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

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(B)

5^{25}

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(C)

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

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(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 $\frac{1}{5^{10}}$ .