# How do you simplify \frac { [ x ^ { 2} \cdot y ^ { - 6} ] ^ { 3} \cdot z ^ { 4} \cdot a ^ { - 9} } { a ^ { 10} \cdot a x ^ { 2} y ^ { - 2} }?

Nov 28, 2017

$\frac{{\left({x}^{2} \cdot {y}^{-} 6\right)}^{3} \cdot {z}^{4} \cdot {a}^{-} 9}{{a}^{10} \cdot a \cdot {x}^{2} \cdot {y}^{-} 2} = \frac{{\left(x \cdot z\right)}^{4}}{{a}^{20} \cdot {y}^{16}}$

#### Explanation:

$\frac{{\left({x}^{2} \cdot {y}^{-} 6\right)}^{3} \cdot {z}^{4} \cdot {a}^{-} 9}{{a}^{10} \cdot a \cdot {x}^{2} \cdot {y}^{-} 2}$

rarr((x^6*y^-18)*z^4*a^-9)/(a^(10+1)*x^2*y^-2

rarr(x^(6-2)*z^4)/(a^(11+9)*y^(18-2)

rarr(x^4*z^4)/(a^20*y^16

rarr((x*z)^4)/(a^20*y^16

Nov 28, 2017

$= \setminus \frac{{x}^{4} \setminus \cdot {z}^{4}}{{y}^{16} \setminus \cdot {a}^{20}}$

#### Explanation:

$\setminus \frac{{\left[{x}^{2} \setminus \cdot {y}^{- 6}\right]}^{3} \setminus \cdot {z}^{4} \setminus \cdot {a}^{- 9}}{{a}^{10} \setminus \cdot a {x}^{2} {y}^{- 2}}$

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

$= \setminus \frac{\left[{x}^{2 \times 3} \setminus \cdot {y}^{- 6 \times 3}\right] \setminus \cdot {z}^{4} \setminus \cdot {a}^{- 9}}{{a}^{10} \setminus \cdot {a}^{1} {x}^{2} {y}^{- 2}}$

Rule:${a}^{m} \times {a}^{n} = {a}^{m + n}$

$= \setminus \frac{{x}^{6} \setminus \cdot {y}^{- 18} \setminus \cdot {z}^{4} \setminus \cdot {a}^{- 9}}{{a}^{10 + 1} \setminus \cdot a {x}^{2} {y}^{- 2}}$

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

$= {x}^{6 - 2} \setminus \cdot {y}^{- 18 + 2} \setminus \cdot {z}^{4} \setminus \cdot {a}^{- 9 - 11}$

$= {x}^{4} \setminus \cdot {y}^{- 16} \setminus \cdot {z}^{4} \setminus \cdot {a}^{- 20}$

or

$= \setminus \frac{{x}^{4} \setminus \cdot {z}^{4}}{{y}^{16} \setminus \cdot {a}^{20}}$