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

To solve the expression $\left(\frac{1}{3}\right)^3$, we need to apply the rule for exponents of a fraction, which states:

$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$

Using this property, we can rewrite the fraction with its exponent as follows:

$\left(\frac{1}{3}\right)^3 = \frac{1^3}{3^3}$

Now, calculate the powers of the numerator and the denominator separately:

• $1^3 = 1$

• $3^3 = 27$

Thus, putting it all together, we have:

$\frac{1^3}{3^3} = \frac{1}{27}$

This shows that raising both the numerator and the denominator of a fraction to a power involves calculating the power of each part separately and then constructing a new fraction.

The solution to the question is: $\frac{1}{27}$