Question

Write your answer as a power or as a product of powers. $$ (-a b)\left(a^{2} b\right)^{2} $$

Short answer

The simplified form of expression \(-a b(a^{2} b)^{2}\) is \(-a^{5}b^{3}

Step-by-step solution

Expand the Expression

First, take the expression \(-a b(a^{2} b)^{2}\) and apply property of exponents which states that \((a^m)^n = a^{m*n}\). So, we get: \(-a b(a^{4}b^{2})\).

Simplify the Expression

Next, apply the property of exponents which states that \( a^m * a^n = a^{m+n}\). So, \(-a b*a^{4}b^{2} = -a^{5}b^{3}\). Thus, the simplified form of given expression is \(-a^{5}b^{3}\).