# How do you simplify (-5^5y^4z^-5)^6/(2^-2y^-2z^3)?

Mar 19, 2018

$\frac{{2}^{2} \cdot {5}^{30} {y}^{26}}{z} ^ 33$

#### Explanation:

${\left(- {5}^{5} {y}^{4} {z}^{-} 5\right)}^{6} / \left({2}^{-} 2 {y}^{-} 2 {z}^{3}\right)$

To avoid confusion, rewrite as

${\left(\left(- 1\right) \cdot {5}^{5} {y}^{4} {z}^{-} 5\right)}^{6} / \left({2}^{-} 2 {y}^{-} 2 {z}^{3}\right)$

Now apply exponent rule ${\left({a}^{n}\right)}^{m} = {a}^{n m}$

$\frac{{\left(- 1\right)}^{6} \cdot {5}^{30} {y}^{24} {z}^{-} 30}{{2}^{-} 2 {y}^{-} 2 {z}^{3}}$

Note that ${\left(- 1\right)}^{6} = 1$ because 6 is even so our expression is now

$\frac{{5}^{30} {y}^{24} {z}^{-} 30}{{2}^{-} 2 {y}^{-} 2 {z}^{3}}$

Using exponent laws we know that $\frac{1}{2} ^ - 2 = {2}^{2} / 1$

$\frac{{2}^{2} \cdot {5}^{30} {y}^{24} {z}^{-} 30}{{y}^{-} 2 {z}^{3}}$

Exponent laws also tell us that ${y}^{24} / {y}^{-} 2 = {y}^{24 - - 2} = {y}^{24 + 2} = {y}^{26}$ so we can write

$\frac{{2}^{2} \cdot {5}^{30} {y}^{26} {z}^{-} 30}{z} ^ 3$

Finally ${z}^{-} \frac{30}{z} ^ 3 = \frac{1}{z} ^ \left(3 - - 30\right) = \frac{1}{z} ^ \left(3 + 30\right) = \frac{1}{z} ^ 33$ so the answer is

$\frac{{2}^{2} \cdot {5}^{30} {y}^{26}}{z} ^ 33$