Evaluate (6/x)³: Complete the Cube of a Fraction Expression

Question

Insert the corresponding expression:

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

00:00 Simplify the following problem

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

00:07 equals the numerator and denominator raised to the same power (N)

00:10 We will apply this formula to our exercise

00:14 We will raise both numerator and denominator to the power (N)

00:17 This is the solution

To solve this problem, we will rewrite the expression $\left(\frac{6}{x}\right)^3$ using the power of a fraction rule. The steps are as follows:

Identify the fraction's numerator $6$ and denominator $x$ .
According to the power of a fraction rule, apply the power 3 to both the numerator and the denominator:
$\left(\frac{6}{x}\right)^3 = \frac{6^3}{x^3}$ .

Therefore, the expression is correctly written as $\frac{6^3}{x^3}$ .

Comparing with the provided answer choices, the correct choice is choice $2$ :

$\frac{6^3}{x^3}$

$\frac{6^3}{x^3}$