Question

Then evaluate the expression when \(a=1\) and \(b=2\). $$ \left(a \cdot b^{2}\right)^{2} $$

Short answer

The final result of evaluating the expression \((a \cdot b^{2})^{2}\) using \(a=1\) and \(b=2\) is 16

Step-by-step solution

Substitute the Given Values in the Expression

Replace the variable \(a\) with 1 and the variable \(b\) with 2 in the given expression to obtain \((1 \cdot 2^{2})^{2}\)

Simplify Inside the Brackets

Calculate the value of \(2^{2}\) which equals 4, then multiply by \(a=1\) to obtain \((1 \cdot 4)^{2} = 4^{2}\)

Calculate the Power

Calculate the value of \(4^{2}\) which equals 16