# How do you simplify ((4a^7b^4)/(8b^2))^3?

Jun 5, 2018

$= \frac{{a}^{21} {b}^{6}}{8}$

#### Explanation:

As per the question, we have

${\left(\frac{4 {a}^{7} {b}^{4}}{8 {b}^{2}}\right)}^{3}$

$= {\left(\frac{\cancel{4} {a}^{7} {b}^{4}}{\cancel{8} 2 {b}^{2}}\right)}^{3}$

$= {\left(\frac{{a}^{7} {\cancel{b}}^{2} \times {b}^{2}}{2 {\cancel{b}}^{2}}\right)}^{3}$

$= {\left(\frac{{a}^{7} {b}^{2}}{2}\right)}^{3}$

Now cubing these terms, we get

$\frac{{a}^{7 \times 3} \times {b}^{2 \times 3}}{2} ^ 3$

$= \frac{{a}^{21} {b}^{6}}{8}$