# How do you simplify and write b^8(2b)^4 with positive exponents?

Jul 19, 2016

${b}^{8} {\left(2 b\right)}^{4} = 16 {b}^{12}$

#### Explanation:

You can look at it this way, in case you ever want to come up with your own formulas:
${\left(2 b\right)}^{4} = 2 b \cdot 2 b \cdot 2 b \cdot 2 b = 16 {b}^{4}$
Or more generally, ${\left(a b\right)}^{n} = {a}^{n} {b}^{n}$
Next,
$\left({b}^{8}\right) \left({b}^{4}\right) = \left(b \cdot b \cdot b \cdot b \cdot b \cdot b \cdot b \cdot b\right) \left(b \cdot b \cdot b \cdot b\right)$
By associativity, we now have:
${b}^{12}$
Hence, more generally, we have ${a}^{m} \cdot {a}^{n} = {a}^{m + n}$
Thus, we get ${b}^{8} {\left(2 b\right)}^{4} = 16 {b}^{12}$