Question

which expression is equivalent to ((5^{-1})^2)?
answer
(\frac{1}{25}) (quad) (125)
(5) (quad) (\frac{1}{125})

Explanation:

Step1: Apply exponent power rule

$(a^m)^n = a^{m \times n}$
So, $(5^{-1})^2 = 5^{-1 \times 2} = 5^{-2}$

Step2: Convert negative exponent to positive

$a^{-n} = \frac{1}{a^n}$
So, $5^{-2} = \frac{1}{5^2}$

Step3: Calculate denominator

$5^2 = 25$
So, $\frac{1}{5^2} = \frac{1}{25}$

Answer:

$\frac{1}{25}$ (corresponding to the first option)