What is [(2x^{-2}y^2*(-x^2))/((2y^4)^4)]^4 ?

The solution to [(2x^{-2}y^2*(-x^2))/((2y^4)^4)]^4 is 1/(4096y^{56)}

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simplify [(2x^{-2}y^2*(-x^2))/((2y^4)^4)]^4

simplify

[\frac{2 x ^{- 2} y ^{2} \cdot ( - x ^{2} )}{( 2 y ^{4} ) ^{4}}]^{4}

\frac{1}{4096 y ^{56}}

Solution steps

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

Apply rule:

a (- b) = - ab

2 x^{- 2} y^{2} (- x^{2}) = - 2 x^{- 2} y^{2} x^{2}

= (\frac{- 2 x ^{- 2} y ^{2} x ^{2}}{( 2 y ^{4} ) ^{4}})^{4}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( - 2 x ^{- 2} y ^{2} x ^{2} ) ^{4}}{( ( 2 y ^{4} ) ^{4} ) ^{4}}

Simplify

(- 2 x^{- 2} y^{2} x^{2})^{4} : 16 y^{8}

= \frac{16 y ^{8}}{( ( 2 y ^{4} ) ^{4} ) ^{4}}

Simplify

((2 y^{4})^{4})^{4} : 65536 y^{64}

= \frac{16 y ^{8}}{65536 y ^{64}}

Cancel the common factor:

16

= \frac{y ^{8}}{4096 y ^{64}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{y ^{8}}{y ^{64}} = \frac{1}{y ^{64 - 8}}

= \frac{1}{4096 y ^{64 - 8}}

Subtract the numbers:

64 - 8 = 56

= \frac{1}{4096 y ^{56}}

\frac{( 5 ^{2} ) ^{3}}{( 5 ^{3} ) ^{7}}

4 x^{2} + 2 x^{2}

\frac{3}{5 - 2}

x^{3} - 64 x^{4}

What is [(2x^{-2}y^2*(-x^2))/((2y^4)^4)]^4 ?
The solution to [(2x^{-2}y^2*(-x^2))/((2y^4)^4)]^4 is 1/(4096y^{56)}