Simplify (8x^-3y*5x^5y)/(10x^6y^2)

$\frac{8 x^{- 3} y \cdot 5 x^{5} y}{10 x^{6} y^{2}}$

Step 1

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

Move $x^{5}$ .

$\frac{8 (x^{5} x^{- 3}) y \cdot (5 y)}{10 x^{6} y^{2}}$

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

$\frac{8 x^{5 - 3} y \cdot (5 y)}{10 x^{6} y^{2}}$

Subtract $3$ from $5$ .

$\frac{8 x^{2} y \cdot (5 y)}{10 x^{6} y^{2}}$

Step 2

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$\frac{8 x^{2} (y \cdot y) \cdot 5}{10 x^{6} y^{2}}$

Multiply $y$ by $y$ .

$\frac{8 x^{2} y^{2} \cdot 5}{10 x^{6} y^{2}}$

Step 3

Cancel the common factor of $8$ and $10$ .

Factor $2$ out of $8 x^{2} y^{2} \cdot 5$ .

$\frac{2 (4 x^{2} y^{2} \cdot 5)}{10 x^{6} y^{2}}$

Cancel the common factors.

Factor $2$ out of $10 x^{6} y^{2}$ .

$\frac{2 (4 x^{2} y^{2} \cdot 5)}{2 (5 x^{6} y^{2})}$

Cancel the common factor.

$\frac{2 (4 x^{2} y^{2} \cdot 5)}{2 (5 x^{6} y^{2})}$

Rewrite the expression.

$\frac{4 x^{2} y^{2} \cdot 5}{5 x^{6} y^{2}}$

Step 4

Cancel the common factor of $x^{2}$ and $x^{6}$ .

Factor $x^{2}$ out of $4 x^{2} y^{2} \cdot 5$ .

$\frac{x^{2} (4 y^{2} \cdot 5)}{5 x^{6} y^{2}}$

Cancel the common factors.

Factor $x^{2}$ out of $5 x^{6} y^{2}$ .

$\frac{x^{2} (4 y^{2} \cdot 5)}{x^{2} (5 x^{4} y^{2})}$

Cancel the common factor.

$\frac{x^{2} (4 y^{2} \cdot 5)}{x^{2} (5 x^{4} y^{2})}$

Rewrite the expression.

$\frac{4 y^{2} \cdot 5}{5 x^{4} y^{2}}$

Step 5

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

Cancel the common factor.

$\frac{4 y^{2} \cdot 5}{5 x^{4} y^{2}}$

Rewrite the expression.

$\frac{4 \cdot 5}{5 x^{4}}$

Step 6

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{4 \cdot 5}{5 x^{4}}$

Rewrite the expression.

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

Simplify (8x^-3y*5x^5y)/(10x^6y^2)

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