What is ((4x^{-3}y^5)^3)/((16x^2y^{-2))^{-4}} ?

The solution to ((4x^{-3}y^5)^3)/((16x^2y^{-2))^{-4}} is (4194304y^7)/x

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simplify ((4x^{-3}y^5)^3)/((16x^2y^{-2))^{-4}}

simplify

\frac{( 4 x ^{- 3} y ^{5} ) ^{3}}{( 16 x ^{2} y ^{- 2} ) ^{- 4}}

\frac{4194304 y ^{7}}{x}

Solution steps

\frac{( 4 x ^{- 3} y ^{5} ) ^{3}}{( 16 x ^{2} y ^{- 2} ) ^{- 4}}

Simplify

(4 x^{- 3} y^{5})^{3} : 4^{3} \cdot \frac{1}{x ^{9}} y^{15}

= \frac{4 ^{3} \cdot \frac{1}{x ^{9}} y ^{15}}{( 16 x ^{2} y ^{- 2} ) ^{- 4}}

Simplify

(16 x^{2} y^{- 2})^{- 4} : 1 6^{- 4} \cdot \frac{1}{x ^{8}} y^{8}

= \frac{4 ^{3} \cdot \frac{1}{x ^{9}} y ^{15}}{1 6 ^{- 4} \cdot \frac{1}{x ^{8}} y ^{8}}

Factor

1 6^{- 4} : 4^{- 8}

= \frac{4 ^{3} \cdot \frac{1}{x ^{9}} y ^{15}}{4 ^{- 8} \cdot \frac{1}{x ^{8}} y ^{8}}

\frac{4 ^{3}}{4 ^{- 8}} = 4^{11}

= \frac{4 ^{11} \cdot \frac{1}{x ^{9}} y ^{15}}{\frac{1}{x ^{8}} y ^{8}}

Simplify

\frac{y ^{15}}{y ^{8}} : y^{7}

= \frac{4 ^{11} \cdot \frac{1}{x ^{9}} y ^{7}}{\frac{1}{x ^{8}}}

Simplify

\frac{4 ^{11} \cdot \frac{1}{x ^{9}} y ^{7}}{\frac{1}{x ^{8}}} : \frac{4194304 y ^{7}}{x}

= \frac{4194304 y ^{7}}{x}

x^{2} - 5 x + 15 = x (x - 3) - 14 + 5 (x - 2) + 3 (13 - 2 x)

x^{2} = 6 x + 91

\frac{1}{2} 12 - \frac{1}{3} 18 + \frac{3}{4} 48 + \frac{1}{6} 72

2 a^{2} - 8 a

- x^{2} - 7 x - 12 \leq - 2

What is ((4x^{-3}y^5)^3)/((16x^2y^{-2))^{-4}} ?
The solution to ((4x^{-3}y^5)^3)/((16x^2y^{-2))^{-4}} is (4194304y^7)/x