Question

Simplify the expression. Then evaluate the expression when \(a=1\) and \(b=2\). $$\left(a^{3} b\right)^{4}$$

Short answer

16

Step-by-step solution

Apply Power of a Product Rule

Use the rule of exponents \((ab)^n = a^n * b^n\) to simplify \(\left(a^{3}b\right)^{4} \)to \(a^{12} b^{4}\).

Substitute Values for a and b

Substitute \(a = 1\) and \(b = 2\) into the simplified expression \(a^{12} b^{4}\) which gives us \(1^{12}*2^{4}\).

Simplify the Expression

Do the calculation to make the final simplification which gives us \(1*16 = 16\).