Evaluate (2/5)^-2

Problem

${\left(\frac{2}{5}\right)}^{-2}$

Solution

1. Apply the negative exponent rule, which states that $a^{-n}=\frac{1}{a^n}$ For a fraction, this means taking the reciprocal of the base and changing the sign of the exponent.

${\left(\frac{2}{5}\right)}^{-2}={\left(\frac{5}{2}\right)}^2$

2. Apply the power of a quotient rule, which states that ${\left(\frac{a}{b}\right)}^n=\frac{a^n}{b^n}$

${\left(\frac{5}{2}\right)}^2=\frac{5^2}{2^2}$

3. Evaluate the powers in the numerator and the denominator.

$\frac{5^2}{2^2}=\frac{25}{4}$

Final Answer

${\left(\frac{2}{5}\right)}^{-2}=\frac{25}{4}$

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