What is xy^{-2}(xy^2-3y^3) ?

The solution to xy^{-2}(xy^2-3y^3) is x(x-3y)

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simplify xy^{-2}(xy^2-3y^3)

simplify

x y^{- 2} (x y^{2} - 3 y^{3})

x (x - 3 y)

Solution steps

x y^{- 2} (x y^{2} - 3 y^{3})

Apply exponent rule:

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

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

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

Apply the fraction rule:

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

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

Apply rule:

a \cdot 1 = a

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

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

Factor

x y^{2} - 3 y^{3} : y^{2} (x - 3 y)

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

Cancel the common factor:

y^{2}

= x (x - 3 y)

(8 ab) (3 a^{2} c)

(3.245 x 1 0^{3} c m) x (2.2 x 1 0^{2} c m)