Simplify (2x^-2y^3)/(3xy^-4)

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

Step 1

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

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

Step 2

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Step 3

Move $y^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 4

Multiply $y^{3}$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

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

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

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

Add $4$ and $3$ .

$\frac{2 y^{7}}{3 x^{3}}$