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

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

Step 1

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

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

Step 2

Cancel the common factor of $y^{4}$ and $y$ .

Factor $y$ out of ${(x^{- 2})}^{3} y^{4} x^{2}$ .

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

Cancel the common factors.

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

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

Factor $y$ out of $y^{1}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide ${(x^{- 2})}^{3} y^{3} x^{2}$ by $1$ .

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

Step 3

Multiply the exponents in ${(x^{- 2})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Multiply $- 2$ by $3$ .

$x^{- 6} y^{3} x^{2}$

Step 4

Multiply $x^{- 6}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$x^{2} x^{- 6} y^{3}$

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

$x^{2 - 6} y^{3}$

Subtract $6$ from $2$ .

$x^{- 4} y^{3}$

Step 5

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{x^{4}} y^{3}$

Step 6

Combine $\frac{1}{x^{4}}$ and $y^{3}$ .

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