Calculate (2/9)^7: Evaluating Powers of Fractions

Question

Insert the corresponding expression:

$\left(\frac{2}{9}\right)^7=$

00:00 Simplify the following problem

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

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

00:11 We will apply this formula to our exercise

00:17 This is the solution

To solve this problem, we'll use the rule for powers of a fraction, which states that $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$ .

Given the expression $\left(\frac{2}{9}\right)^7$ , we apply this exponent rule:

$\left(\frac{2}{9}\right)^7 = \frac{2^7}{9^7}$

This means we raise the numerator, 2, to the power of 7, and the denominator, 9, also to the power of 7.

The matching choice in the given options is:

Therefore, the solution to the problem is $\frac{2^7}{9^7}$ .

$\frac{2^7}{9^7}$