What is (2x^3y^2)^{-2}(1/3 x^3y)^2 ?

The solution to (2x^3y^2)^{-2}(1/3 x^3y)^2 is 1/(36y^2)

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simplify (2x^3y^2)^{-2}(1/3 x^3y)^2

simplify

(2 x^{3} y^{2})^{- 2} (\frac{1}{3} x^{3} y)^{2}

\frac{1}{36 y ^{2}}

Solution steps

(2 x^{3} y^{2})^{- 2} (\frac{1}{3} x^{3} y)^{2}

Simplify

(2 x^{3} y^{2})^{- 2} : \frac{1}{4 x ^{6} y ^{4}}

= \frac{1}{4 x ^{6} y ^{4}} (\frac{1}{3} x^{3} y)^{2}

Simplify

(\frac{1}{3} x^{3} y)^{2} : \frac{x ^{6} y ^{2}}{9}

= \frac{1}{4 x ^{6} y ^{4}} \cdot \frac{x ^{6} y ^{2}}{9}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot x ^{6} y ^{2}}{4 x ^{6} y ^{4} \cdot 9}

Apply rule:

1 \cdot a = a

1 \cdot x^{6} y^{2} = x^{6} y^{2}

= \frac{x ^{6} y ^{2}}{4 x ^{6} y ^{4} \cdot 9}

Cancel the common factor:

x^{6}

= \frac{y ^{2}}{4 y ^{4} \cdot 9}

Simplify

\frac{y ^{2}}{y ^{4}} : \frac{1}{y ^{2}}

= \frac{1}{4 y ^{2} \cdot 9}

Multiply the numbers:

4 \cdot 9 = 36

= \frac{1}{36 y ^{2}}

1 + 8 a^{3}

- x^{2} + 1 > x + 1

r^{2} + 36 r = 0

f (y) = 3 y^{2} + 12 y + 4

(18 + 2 x) (26 + 2 x) = 1140

What is (2x^3y^2)^{-2}(1/3 x^3y)^2 ?
The solution to (2x^3y^2)^{-2}(1/3 x^3y)^2 is 1/(36y^2)