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

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:

• Choice 1: $\frac{2^7}{9^7}$

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