Solve (10/13)^(-4): Negative Exponent Calculation

Question

Insert the corresponding expression:

$\left(\frac{10}{13}\right)^{-4}=$

00:00 Simplify the following problem

00:03 According to the laws of exponents, a fraction raised to the power (N)

00:09 equals the numerator and denominator, each raised to the same power (N)

00:13 We will apply this formula to our exercise

00:17 This is the solution

To solve the expression $\left(\frac{10}{13}\right)^{-4}$ , we start by applying the rule for dividing exponents is:

$\frac{10^{-4}}{13^{-4}}$ , which maintains the negative exponent but as separate components of fraction resulting in the same value.

Consequently, the expression $\left(\frac{10}{13}\right)^{-4}$ equates to $\frac{10^{-4}}{13^{-4}}$ .

By comparing this with the presented choices, we identify that option (2):

$\frac{10^{-4}}{13^{-4}}$

matches correctly with our conversion of the original expression.

Therefore, the correct expression is $\frac{10^{-4}}{13^{-4}}$ .

$\frac{10^{-4}}{13^{-4}}$