Evaluate (1/9)^7: Solving Powers of Fraction Expression

To solve this problem, we'll apply the formula for the power of a quotient:

• Step 1: Identify the expression $\frac{1^7}{9^7}$.
• Step 2: Recognize that $\frac{a^n}{b^n} = \left( \frac{a}{b} \right)^n$ applies here. The numerator is $a^7 = 1^7$, and the denominator is $b^7 = 9^7$.
• Step 3: Apply the formula: $\frac{1^7}{9^7} = \left( \frac{1}{9} \right)^7$.

In step 2, we used the property that allows us to rewrite $\frac{1^7}{9^7}$ as $\left( \frac{1}{9} \right)^7$, which is more convenient for interpretation or further calculations.

Therefore, the expression $\frac{1^7}{9^7}$ can be rewritten as $\left( \frac{1}{9} \right)^7$.