The problem asks us to simplify the expression $\left(\frac{-a}{b^2}\right)^3$.

1. Problem Description

The problem asks us to simplify the expression $\left(\frac{-a}{b^2}\right)^3$.

2. Solution Steps

To simplify the expression, we need to raise both the numerator and the denominator to the power of

3.

$\left(\frac{x}{y}\right)^n = \frac{x^n}{y^n}$

Applying this rule, we get

$\left(\frac{-a}{b^2}\right)^3 = \frac{(-a)^3}{(b^2)^3}$

$(-a)^3 = (-1)^3 \cdot a^3 = -a^3$

$(b^2)^3 = b^{2 \cdot 3} = b^6$

Therefore,

$\frac{(-a)^3}{(b^2)^3} = \frac{-a^3}{b^6}$

3. Final Answer

The simplified expression is $-\frac{a^3}{b^6}$.