Question

Then evaluate the expression when \(a=1\) and \(b=2\). $$ \left(a^{2} b\right)^{4} $$

Short answer

The value of \(\left(a^{2} b\right)^{4}\) when \(a=1\) and \(b=2\) is 16

Step-by-step solution

Apply the Power of Power Rule

Apply the power of power rule. Given \(\left(a^{2} b\right)^{4}\), the rule implies \((a^{2*4})*(b^{4}) = a^{8}b^{4}\)

Substitute the Given Values

Substitute the given values \(a=1\) and \(b=2\) into the equation. This gives \(a^{8}b^{4} = 1^{8} * 2^{4}\)

Evaluate the Expression

Evaluate the expression. Hence, \(1^{8} * 2^{4} = 1 * 16 = 16\)