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Which expression is equivalent to
((5^(-1))/(5^(0)))^(-3)?
25
125
0

(1)/(125)

Which expression is equivalent to $\left(\frac{5^{-1}}{5^{0}}\right)^{-3} ?$ $\newline$ $25$ $\newline$ $125$ $\newline$ $0$ $\newline$ $\frac{1}{125}$

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Multiplication with rational exponents

Full solution

Q. Which expression is equivalent to

\left(\frac{5^{-1}}{5^{0}}\right)^{-3} ?

\newline

25

\newline

125

\newline

0

\newline

\frac{1}{125}

Simplify base: Simplify the base of the expression. $\newline$ We have the expression $((5^{-1})/(5^{0}))^{-3}$ . First, we need to simplify the base $(5^{-1})/(5^{0})$ . $\newline$ Since any number to the power of $0$ is $1$ , we have $5^{0} = 1$ . $\newline$ So, the base simplifies to $5^{-1}/1$ , which is just $5^{-1}$ .
Apply negative exponent: Apply the negative exponent to the base. $\newline$ Now we have $(5^{-1})^{-3}$ . When we raise a power to a power, we multiply the exponents. $\newline$ So, $(-1) \times (-3) = 3$ . $\newline$ Therefore, the expression simplifies to $5^3$ .
Calculate value: Calculate the value of $5^3$ . $5^3$ means $5$ multiplied by itself $3$ times. So, $5 \times 5 \times 5 = 125$ .

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