Simplify (4xy^-2)/(-3yx^2*-2y^0)

$\frac{4 x y^{- 2}}{- 3 y x^{2} \cdot - 2 y^{0}}$

Step 1

Multiply $y$ by $y^{0}$ by adding the exponents.

Move $y^{0}$ .

$\frac{4 x y^{- 2}}{- 3 (y^{0} y) x^{2} \cdot - 2}$

Multiply $y^{0}$ by $y$ .

Raise $y$ to the power of $1$ .

$\frac{4 x y^{- 2}}{- 3 (y^{0} y^{1}) x^{2} \cdot - 2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 x y^{- 2}}{- 3 y^{0 + 1} x^{2} \cdot - 2}$

Add $0$ and $1$ .

$\frac{4 x y^{- 2}}{- 3 y^{1} x^{2} \cdot - 2}$

Step 2

Simplify $- 3 y^{1} x^{2} \cdot - 2$ .

$\frac{4 x y^{- 2}}{- 3 y x^{2} \cdot - 2}$

Step 3

Move $y^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4 x}{- 3 y x^{2} \cdot - 2 y^{2}}$

Step 4

Multiply $y$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

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

Multiply $y^{2}$ by $y$ .

Raise $y$ to the power of $1$ .

$\frac{4 x}{- 3 (y^{2} y^{1}) x^{2} \cdot - 2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 x}{- 3 y^{2 + 1} x^{2} \cdot - 2}$

Add $2$ and $1$ .

$\frac{4 x}{- 3 y^{3} x^{2} \cdot - 2}$

Step 5

Cancel the common factor of $4$ and $- 2$ .

Factor $2$ out of $4 x$ .

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

Cancel the common factors.

Factor $2$ out of $- 3 y^{3} x^{2} \cdot - 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{2 x}{- 3 y^{3} x^{2} \cdot - 1}$

Step 6

Cancel the common factor of $x$ and $x^{2}$ .

Factor $x$ out of $2 x$ .

$\frac{x \cdot 2}{- 3 y^{3} x^{2} \cdot - 1}$

Cancel the common factors.

Factor $x$ out of $- 3 y^{3} x^{2} \cdot - 1$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{2}{- 3 y^{3} x \cdot - 1}$

Step 7

Multiply $- 1$ by $- 3$ .

$\frac{2}{3 y^{3} x}$

Simplify (4xy^-2)/(-3yx^2*-2y^0)

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