Simplify x^-3y^2x^-4y^24y^-1

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

Step 1

Rewrite using the commutative property of multiplication.

$4 x^{- 3} y^{2} x^{- 4} y^{2} y^{- 1}$

Step 2

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

Move $x^{- 4}$ .

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

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

$4 x^{- 4 - 3} y^{2} y^{2} y^{- 1}$

Subtract $3$ from $- 4$ .

$4 x^{- 7} y^{2} y^{2} y^{- 1}$

Step 3

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

Move $y^{2}$ .

$4 x^{- 7} (y^{2} y^{2}) y^{- 1}$

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

$4 x^{- 7} y^{2 + 2} y^{- 1}$

Add $2$ and $2$ .

$4 x^{- 7} y^{4} y^{- 1}$

Step 4

Multiply $y^{4}$ by $y^{- 1}$ by adding the exponents.

Move $y^{- 1}$ .

$4 x^{- 7} (y^{- 1} y^{4})$

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

$4 x^{- 7} y^{- 1 + 4}$

Add $- 1$ and $4$ .

$4 x^{- 7} y^{3}$

Step 5

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

$4 \frac{1}{x^{7}} y^{3}$

Step 6

Combine $4$ and $\frac{1}{x^{7}}$ .

$\frac{4}{x^{7}} y^{3}$

Step 7

Combine $\frac{4}{x^{7}}$ and $y^{3}$ .

$\frac{4 y^{3}}{x^{7}}$

Simplify x^-3y^2*x^-4y^2*4y^-1