# How do you simplify (- 3x ^ { - 4} y z ^ { - 7} ) ^ { 2} ( 4x y ^ { 5} z ^ { - 2} z ^ { - 2} ) ^ { 3}?

##### 1 Answer
May 12, 2018

(-3x^(-4)yz^(-7))^2(4xy^5z^(-2)z^(-2))^3=color(blue)((576y^17)/(x^5z^26)

#### Explanation:

Simplify:

${\left(- 3 {x}^{- 4} y {z}^{- 7}\right)}^{2} {\left(4 x {y}^{5} {z}^{- 2} {z}^{- 2}\right)}^{3}$

Apply power rule: ${\left({a}^{m}\right)}^{n} = {a}^{m \cdot n}$

$\left(- {3}^{2} {x}^{- 4 \cdot 2} {y}^{1 \cdot 2} {z}^{- 7 \cdot 2}\right) \left({4}^{3} {x}^{1 \cdot 3} {y}^{5 \cdot 3} {z}^{- 2 \cdot 3} {z}^{- 2 \cdot 3}\right)$

Simplify.

$9 {x}^{- 8} {y}^{2} {z}^{- 14} 64 {x}^{3} {y}^{15} {z}^{- 6} {z}^{- 6}$

Collect like terms.

$9 \times 64 {x}^{- 8} {x}^{3} {y}^{2} {y}^{15} {z}^{- 14} {z}^{- 6} {z}^{- 6}$

Simplify $9 \times 64$ to $576$.

$576 {x}^{- 8} {x}^{3} {y}^{2} {y}^{15} {z}^{- 14} {z}^{- 6} {z}^{- 6}$

Apply product rule: ${a}^{m} {a}^{n} = {a}^{m + n}$

$576 {x}^{- 8 + 3} {y}^{2 + 15} {z}^{- 14 + \left(- 6\right) + \left(- 6\right)}$

Simplify.

$576 {x}^{- 5} {y}^{17} {z}^{- 26}$

Apply negative exponent rule: ${a}^{- m} = \frac{1}{a} ^ m$

$\frac{576 {y}^{17}}{{x}^{5} {z}^{26}}$