# How do you use the laws of exponents to simplify the expression (6y^3)^4/(2y^5)?

May 9, 2015

The Laws of Exponents relevant here are
1. ${\left(b c\right)}^{m} = {b}^{m} \cdot {c}^{m}$
2. ${\left({b}^{m}\right)}^{n} = {b}^{m n}$
3. ${b}^{- m} = \frac{1}{{b}^{m}}$
4. ${b}^{m} \cdot {b}^{n} = {b}^{m + n}$

$\frac{{\left({\left(6 y\right)}^{3}\right)}^{4}}{2 {y}^{5}}$

$= \frac{{\left(6 y\right)}^{12}}{2 {y}^{5}} \text{ by Rule [2]}$

$= \frac{{6}^{12} \cdot {y}^{12}}{2 {y}^{5}} \text{ by Rule [1]}$

$= {6}^{12} / 2 \cdot {y}^{12} \cdot {y}^{- 5} \text{ by Rule [3]}$

$= {6}^{12} / 2 {y}^{7} \text{ by Rule [4]}$

You could evaluate ${6}^{12} / 2$ but that's just arithmetic.