What is ((-8x^2y^2)^2)/((4x^3y)^3) ?

The solution to ((-8x^2y^2)^2)/((4x^3y)^3) is y/(x^5)

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simplify ((-8x^2y^2)^2)/((4x^3y)^3)

simplify

\frac{( - 8 x ^{2} y ^{2} ) ^{2}}{( 4 x ^{3} y ) ^{3}}

\frac{y}{x ^{5}}

Solution steps

\frac{( - 8 x ^{2} y ^{2} ) ^{2}}{( 4 x ^{3} y ) ^{3}}

Simplify

(4 x^{3} y)^{3} : 64 x^{9} y^{3}

= \frac{( - 8 x ^{2} y ^{2} ) ^{2}}{64 x ^{9} y ^{3}}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

(- 8 x^{2} y^{2})^{2} = (8 x^{2} y^{2})^{2}

= \frac{( 8 x ^{2} y ^{2} ) ^{2}}{64 x ^{9} y ^{3}}

Simplify

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

= \frac{8 ^{2} x ^{4} y ^{4}}{64 x ^{9} y ^{3}}

Factor the number:

64 = 8^{2}

= \frac{8 ^{2} x ^{4} y ^{4}}{8 ^{2} x ^{9} y ^{3}}

Cancel the common factor:

8^{2}

= \frac{x ^{4} y ^{4}}{x ^{9} y ^{3}}

Simplify

\frac{y ^{4}}{y ^{3}} : y

= \frac{x ^{4} y}{x ^{9}}

Simplify

\frac{x ^{4}}{x ^{9}} : \frac{1}{x ^{5}}

= \frac{y}{x ^{5}}

x^{2} + 5 x + 25 = 0

\frac{1}{6} (6)

1 + 3 ∣ 2 x - 5 ∣ = 4

x^{2} - 3 x y + \frac{1}{2} y^{2}

∣ 2 x + 5 ∣ < 13

What is ((-8x^2y^2)^2)/((4x^3y)^3) ?
The solution to ((-8x^2y^2)^2)/((4x^3y)^3) is y/(x^5)