# How do you simplify (3y^4)^5/y^-6?

Jun 4, 2018

$243 {y}^{26}$

#### Explanation:

We get
${\left(3 {y}^{4}\right)}^{5} = {3}^{5} {y}^{20}$
so
$\frac{{3}^{5} {y}^{20}}{y} ^ \left(- 6\right) = 243 \cdot {y}^{26}$

Jun 4, 2018

$= 243 {y}^{26}$

#### Explanation:

First rule of exponents we use is:

${\left({a}^{n}\right)}^{m} = {a}^{n \cdot m}$

$= {\left(3 {y}^{4}\right)}^{5} / {y}^{-} 6$

$= \frac{{3}^{1 \cdot 5} {y}^{4 \cdot 5}}{y} ^ - 6$

$= \frac{{3}^{5} {y}^{20}}{y} ^ - 6$

$= \frac{243 {y}^{20}}{y} ^ - 6$

New we use the rule for quotients of exponents:

${a}^{n} / {a}^{m} = {a}^{n - m}$

$= \frac{243 {y}^{20}}{y} ^ - 6$

$= 243 {y}^{20 - \left(- 6\right)}$

$= 243 {y}^{26}$