# How do you simplify (\frac { 4x ^ { 6} y ^ { 7} } { 8x ^ { 3} } ) ^ { 4}?

Jun 21, 2017

$\frac{{x}^{12} {y}^{28}}{16}$

#### Explanation:

1. Distribute the exponent of 4 - multiply every exponent inside the parentheses by 4.

Remember, the numbers without exponents actually have an exponent of 1.

${\left(\frac{{4}^{4} {x}^{6} {y}^{7}}{8 {x}^{3}}\right)}^{4}$

$= \frac{{4}^{4} {x}^{24} {y}^{28}}{{8}^{4} {x}^{12}}$

2. ${8}^{4}$, which is 4096, can be rewritten as ${4}^{6}$.

$= \frac{{4}^{4} {x}^{24} {y}^{28}}{{4}^{6} {x}^{12}}$

3. Use the exponent rules to simplify. When dividing powers with the same base, subtract the exponents.

$= {4}^{-} 2 {x}^{12} {y}^{28}$

This can be rewritten as

$= \frac{{x}^{12} {y}^{28}}{{4}^{2}}$

$= \frac{{x}^{12} {y}^{28}}{16}$