Evaluate (2/5)^(-2): Negative Exponent Fraction Problem

Question

Insert the corresponding expression:

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

00:00 Simplify the following problem

00:04 According to the exponent laws, a fraction raised to a power(-N)

00:08 equals the reciprocal fraction raised to the opposite power (N)

00:12 We will apply this formula to our exercise

00:15 We will invert the fraction

00:19 and proceed to raise it to the opposite power (times(-1))

00:23 This is the solution

To solve the problem of converting $\left(\frac{2}{5}\right)^{-2}$ to positive exponents, we use the rule for negative exponents:

Negative exponent rule states:

$\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n$ — This indicates that we invert the fraction and change the sign of the exponent to positive.

Given expression: $\left(\frac{2}{5}\right)^{-2}$ .

Application: By using the rule, the negative exponent instructs us to reciprocate the fraction:

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

The positive exponent $(2)$ indicates the expression is squared. Thus, our action is complete with no further action required.

Thus, the correctly transformed expression of $\left(\frac{2}{5}\right)^{-2}$ is indeed:

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

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