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Which expressions are equivalent to $\newline$ $\frac{5^{2}}{5^{8}}$ ? $\newline$ Choose $2$ answers: $\newline$ A $\frac{1}{5^{6}}$ $\newline$ B $1^{-6}$ $\newline$ C. $(5^{2})^{-3}$ $\newline$ D $(5^{2})^{-8}$

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Multiplication with rational exponents

Full solution

Q. Which expressions are equivalent to

\newline

\frac{5^{2}}{5^{8}}

?

\newline

Choose

2

answers:

\newline

A

\frac{1}{5^{6}}

\newline

B

1^{-6}

\newline

C.

(5^{2})^{-3}

\newline

D

(5^{2})^{-8}

Simplify Expression: Simplify the given expression using the properties of exponents. $\newline$ Calculation: $(5^{2})/(5^{8}) = 5^{2-8} = 5^{-6}$
Compare with Options: Compare the simplified expression to each option. $\newline$ Calculation: $5^{-6}$ matches with option A $(1)/(5^{6})$ because $1/(5^6) = 5^{-6}$ .
Check Option B: Check option B. $\newline$ Calculation: $1^{(-6)}$ simplifies to $1$ , not $5^{(-6)}$ .
Check Option C: Check option C. $\newline$ Calculation: $(5^{2})^{(-3)} = 5^{2*(-3)} = 5^{-6}$ , which matches.
Check Option D: Check option D. $\newline$ Calculation: $(5^{2})^{(-8)} = 5^{2*(-8)} = 5^{-16}$ , which does not match.

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