What is ((2x*y^2)^5)/(((4x^2*y)^2)*(x*y^3)) ?

The solution to ((2x*y^2)^5)/(((4x^2*y)^2)*(x*y^3)) is 2y^5

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simplify ((2xy^2)^5)/(((4x^2y)^2)(xy^3))

simplify

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

2 y^{5}

Solution steps

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

Apply rule:

(a) = a

((4 x^{2} y)^{2}) = (4 x^{2} y)^{2}

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

Simplify

(2 x y^{2})^{5} : 32 x^{5} y^{10}

= \frac{32 x ^{5} y ^{10}}{( 4 x ^{2} y ) ^{2} x y ^{3}}

Simplify

\frac{x ^{5}}{x} : x^{4}

= \frac{32 x ^{4} y ^{10}}{( 4 x ^{2} y ) ^{2} y ^{3}}

Simplify

\frac{y ^{10}}{y ^{3}} : y^{7}

= \frac{32 x ^{4} y ^{7}}{( 4 x ^{2} y ) ^{2}}

Simplify

(4 x^{2} y)^{2} : 4^{2} x^{4} y^{2}

= \frac{32 x ^{4} y ^{7}}{4 ^{2} x ^{4} y ^{2}}

Factor

32 : 4^{2} \cdot 2

= \frac{4 ^{2} \cdot 2 x ^{4} y ^{7}}{4 ^{2} x ^{4} y ^{2}}

Cancel the common factor:

4^{2}

= \frac{2 x ^{4} y ^{7}}{x ^{4} y ^{2}}

Cancel the common factor:

x^{4}

= \frac{2 y ^{7}}{y ^{2}}

Simplify

\frac{y ^{7}}{y ^{2}} : y^{5}

= 2 y^{5}

\frac{( a ^{2} + b ^{2} )}{( b ^{2} )}

8 x^{4} y^{3} z^{2} - 6 x^{3} y^{2} z

5 x + 2 y - 3 x + 5 y - 12 x

\frac{( sin ^{2} ( x ) - cos ^{2} ( x ) )}{( tan ^{2} ( x ) - 1 )}

(2 p + q)^{3} - (p + 2 q)^{3}

What is ((2x*y^2)^5)/(((4x^2*y)^2)*(x*y^3)) ?
The solution to ((2x*y^2)^5)/(((4x^2*y)^2)*(x*y^3)) is 2y^5