A Power of a Quotient

The same idea works for a fraction. $\frac{x}{y}^{3}$ means three copies of the fraction multiplied together: $\frac{\frac{\frac{x}{y}x}{y}x}{y}$. To multiply fractions, multiply the numerators together and the denominators together, which gives $\frac{x^{3}}{y^{3}}$.

To raise a fraction to a power, raise both the numerator and the denominator to that power: $\frac{a}{b}^{n} = \frac{a^{n}}{b^{n}}$, where $b$ is not zero. The example shows that each copy of the fraction adds one factor on top and one factor on the bottom.

Products, quotients and nested powers all let the exponent pass inside. A sum does not. A later chapter on multiplying shows what really happens to $\left(a+b\right)^{2}$.