Solve (10/13) Raised to Negative 2 Power: Fraction Exponent Practice

Question

Insert the corresponding expression:

$\left(\frac{10}{13}\right)^{-2}=$

00:00 Simplify the following problem

00:04 According to the laws of exponents, any fraction raised to the negative exponent (-N)

00:08 equals the reciprocal fraction with the same exponent (N) multiplied by (-1)

00:15 We will apply this formula to our exercise

00:22 This is the solution

To solve the problem, apply the negative exponent rule:

For any fraction $\frac{a}{b}$ with a negative exponent $-n$ , apply the rule: $\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^{n}$ .

Apply this rule to the given expression $\left(\frac{10}{13}\right)^{-2}$ :

$\left(\frac{10}{13}\right)^{-2} = \left(\frac{13}{10}\right)^{2}$

Therefore, the correct expression with a positive exponent is $\left(\frac{13}{10}\right)^{2}$ .

In the provided choices, this is option:

Hence, the correct expression is $\left(\frac{13}{10}\right)^2$ .

$\left(\frac{13}{10}\right)^2$