Calculate (1/5)³: Solving the Cube of a Simple Fraction

To solve this problem, we need to simplify the expression $\left(\frac{1}{5}\right)^3$ using the exponent rules for fractions:

• Step 1: Identify the base and the exponent. Here, the base is $\frac{1}{5}$ and the exponent is $3$.
• Step 2: Apply the rule for raising a fraction to a power. The rule states that $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$.
• Step 3: Apply the exponent to both the numerator and the denominator:

Thus, $\left(\frac{1}{5}\right)^3 = \frac{1^3}{5^3}$.

Therefore, the simplified expression is $\frac{1^3}{5^3}$, which corresponds to choice 1 in the provided options.