# How do you use the laws of exponents to simplify the expression b^8(2b)^4?

May 19, 2015

One law of the exponents states that ${\left({a}^{n}\right)}^{m} = {a}^{n} \cdot m$

Then,

${b}^{8} {\left({2}^{1} {b}^{1}\right)}^{4} = {b}^{8} \left({2}^{1 \cdot 4} {b}^{1 \cdot 4}\right)$

Now, we get ${b}^{8} \left(16 {b}^{4}\right) = 16 \cdot {b}^{8} \cdot {b}^{4}$.

Another law of exponents states that ${a}^{n} \cdot {a}^{m} = {a}^{n + m}$. Thus,

$16 \cdot {b}^{8 + 4} = 16 {b}^{12}$