# How do you simplify [2a^4b]^3/(24b^5)?

Jun 15, 2015

Expand the numerator then (by grouping) simplify the fraction to get
$\frac{{a}^{12}}{3 {b}^{2}}$

#### Explanation:

$\frac{{\left[2 {a}^{4} b\right]}^{3}}{24 {b}^{5}}$

$= \frac{8 {a}^{12} {b}^{3}}{24 {b}^{5}}$

$= \left(\frac{8}{24}\right) \cdot \left(\frac{{a}^{12}}{1}\right) \cdot \left(\frac{{b}^{3}}{{b}^{5}}\right)$

$= \left(\frac{1}{3}\right) \cdot \left(\frac{{a}^{12}}{1}\right) \cdot \left(\frac{1}{{b}^{2}}\right)$

$= \frac{{a}^{12}}{3 {b}^{2}}$