Evaluate (5/6)^(-3): Negative Exponent Expression Solution

Question

Insert the corresponding expression:

$\left(\frac{5}{6}\right)^{-3}=$

00:00 Simplify the following problem

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

00:07 is equal to its reciprocal raised to the opposite power (N)

00:12 We'll apply this formula to our exercise

00:15 Let's invert the fraction

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

00:22 This is the solution

To solve this problem, we need to convert the expression $\left(\frac{5}{6}\right)^{-3}$ into a form with positive exponents.

The negative exponent rule states that $x^{-n} = \frac{1}{x^n}$ . Applying this to our given fraction:

$\left(\frac{5}{6}\right)^{-3} = \left(\frac{6}{5}\right)^{3}$ .

This means we take the reciprocal of $\frac{5}{6}$ , which is $\frac{6}{5}$ , and then raise it to the power of 3.

Therefore, the correct expression is $\left(\frac{6}{5}\right)^3$ .

This matches choice 1 in the list of possible answers.

$\left(\frac{6}{5}\right)^3$