Simplify (8x^4y^5x^-6y^-7)/(4x^2y^3x^-4y^-5)

$\frac{8 x^{4} y^{5} x^{- 6} y^{- 7}}{4 x^{2} y^{3} x^{- 4} y^{- 5}}$

Step 1

Multiply $x^{4}$ by $x^{- 6}$ by adding the exponents.

Move $x^{- 6}$ .

$\frac{8 (x^{- 6} x^{4}) y^{5} y^{- 7}}{4 x^{2} y^{3} x^{- 4} y^{- 5}}$

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

$\frac{8 x^{- 6 + 4} y^{5} y^{- 7}}{4 x^{2} y^{3} x^{- 4} y^{- 5}}$

Add $- 6$ and $4$ .

$\frac{8 x^{- 2} y^{5} y^{- 7}}{4 x^{2} y^{3} x^{- 4} y^{- 5}}$

Step 2

Multiply $y^{5}$ by $y^{- 7}$ by adding the exponents.

Move $y^{- 7}$ .

$\frac{8 x^{- 2} (y^{- 7} y^{5})}{4 x^{2} y^{3} x^{- 4} y^{- 5}}$

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

$\frac{8 x^{- 2} y^{- 7 + 5}}{4 x^{2} y^{3} x^{- 4} y^{- 5}}$

Add $- 7$ and $5$ .

$\frac{8 x^{- 2} y^{- 2}}{4 x^{2} y^{3} x^{- 4} y^{- 5}}$

Step 3

Multiply $x^{2}$ by $x^{- 4}$ by adding the exponents.

Move $x^{- 4}$ .

$\frac{8 x^{- 2} y^{- 2}}{4 (x^{- 4} x^{2}) y^{3} y^{- 5}}$

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

$\frac{8 x^{- 2} y^{- 2}}{4 x^{- 4 + 2} y^{3} y^{- 5}}$

Add $- 4$ and $2$ .

$\frac{8 x^{- 2} y^{- 2}}{4 x^{- 2} y^{3} y^{- 5}}$

Step 4

Multiply $y^{3}$ by $y^{- 5}$ by adding the exponents.

Move $y^{- 5}$ .

$\frac{8 x^{- 2} y^{- 2}}{4 x^{- 2} (y^{- 5} y^{3})}$

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

$\frac{8 x^{- 2} y^{- 2}}{4 x^{- 2} y^{- 5 + 3}}$

Add $- 5$ and $3$ .

$\frac{8 x^{- 2} y^{- 2}}{4 x^{- 2} y^{- 2}}$

Step 5

Cancel the common factor of $8$ and $4$ .

Factor $4$ out of $8 x^{- 2} y^{- 2}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 6

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{2 y^{- 2}}{y^{- 2}}$

Step 7

Cancel the common factor of $y^{- 2}$ .

Cancel the common factor.

$\frac{2 y^{- 2}}{y^{- 2}}$

Divide $2$ by $1$ .

$2$

Simplify (8x^4y^5x^-6y^-7)/(4x^2y^3x^-4y^-5)

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