Simplify ((10x)/(25x^3y^2))÷((32x^7y^4)/(20x^9y^9))

$\frac{10 x}{25 x^{3} y^{2}} \div \frac{32 x^{7} y^{4}}{20 x^{9} y^{9}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{10 x}{25 x^{3} y^{2}} \cdot \frac{20 x^{9} y^{9}}{32 x^{7} y^{4}}$

Step 2

Combine.

$\frac{10 x (20 x^{9} y^{9})}{25 x^{3} y^{2} (32 x^{7} y^{4})}$

Step 3

Multiply $x$ by $x^{9}$ by adding the exponents.

Move $x^{9}$ .

$\frac{10 (x^{9} x) (20 y^{9})}{25 x^{3} y^{2} (32 x^{7} y^{4})}$

Multiply $x^{9}$ by $x$ .

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

$\frac{10 (x^{9} x^{1}) (20 y^{9})}{25 x^{3} y^{2} (32 x^{7} y^{4})}$

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

$\frac{10 x^{9 + 1} (20 y^{9})}{25 x^{3} y^{2} (32 x^{7} y^{4})}$

Add $9$ and $1$ .

$\frac{10 x^{10} (20 y^{9})}{25 x^{3} y^{2} (32 x^{7} y^{4})}$

Step 4

Multiply $x^{3}$ by $x^{7}$ by adding the exponents.

Move $x^{7}$ .

$\frac{10 x^{10} (20 y^{9})}{25 (x^{7} x^{3}) y^{2} (32 y^{4})}$

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

$\frac{10 x^{10} (20 y^{9})}{25 x^{7 + 3} y^{2} (32 y^{4})}$

Add $7$ and $3$ .

$\frac{10 x^{10} (20 y^{9})}{25 x^{10} y^{2} (32 y^{4})}$

Step 5

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

Move $y^{4}$ .

$\frac{10 x^{10} (20 y^{9})}{25 x^{10} (y^{4} y^{2}) \cdot 32}$

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

$\frac{10 x^{10} (20 y^{9})}{25 x^{10} y^{4 + 2} \cdot 32}$

Add $4$ and $2$ .

$\frac{10 x^{10} (20 y^{9})}{25 x^{10} y^{6} \cdot 32}$

Step 6

Cancel the common factor of $10$ and $25$ .

Factor $5$ out of $10 x^{10} (20 y^{9})$ .

$\frac{5 (2 x^{10} (20 y^{9}))}{25 x^{10} y^{6} \cdot 32}$

Cancel the common factors.

Factor $5$ out of $25 x^{10} y^{6} \cdot 32$ .

$\frac{5 (2 x^{10} (20 y^{9}))}{5 (5 x^{10} y^{6} \cdot 32)}$

Cancel the common factor.

$\frac{5 (2 x^{10} (20 y^{9}))}{5 (5 x^{10} y^{6} \cdot 32)}$

Rewrite the expression.

$\frac{2 x^{10} (20 y^{9})}{5 x^{10} y^{6} \cdot 32}$

Step 7

Cancel the common factor of $2$ and $32$ .

Factor $2$ out of $2 x^{10} (20 y^{9})$ .

$\frac{2 (x^{10} (20 y^{9}))}{5 x^{10} y^{6} \cdot 32}$

Cancel the common factors.

Factor $2$ out of $5 x^{10} y^{6} \cdot 32$ .

$\frac{2 (x^{10} (20 y^{9}))}{2 (5 x^{10} y^{6} \cdot 16)}$

Cancel the common factor.

$\frac{2 (x^{10} (20 y^{9}))}{2 (5 x^{10} y^{6} \cdot 16)}$

Rewrite the expression.

$\frac{x^{10} (20 y^{9})}{5 x^{10} y^{6} \cdot 16}$

Step 8

Cancel the common factor of $x^{10}$ .

Cancel the common factor.

$\frac{x^{10} (20 y^{9})}{5 x^{10} y^{6} \cdot 16}$

Rewrite the expression.

$\frac{20 y^{9}}{5 y^{6} \cdot 16}$

Step 9

Cancel the common factor of $20$ and $5$ .

Factor $5$ out of $20 y^{9}$ .

$\frac{5 (4 y^{9})}{5 y^{6} \cdot 16}$

Cancel the common factors.

Factor $5$ out of $5 y^{6} \cdot 16$ .

$\frac{5 (4 y^{9})}{5 (y^{6} \cdot 16)}$

Cancel the common factor.

$\frac{5 (4 y^{9})}{5 (y^{6} \cdot 16)}$

Rewrite the expression.

$\frac{4 y^{9}}{y^{6} \cdot 16}$

Step 10

Cancel the common factor of $4$ and $16$ .

Factor $4$ out of $4 y^{9}$ .

$\frac{4 (y^{9})}{y^{6} \cdot 16}$

Cancel the common factors.

Factor $4$ out of $y^{6} \cdot 16$ .

$\frac{4 (y^{9})}{4 (y^{6} \cdot 4)}$

Cancel the common factor.

$\frac{4 y^{9}}{4 (y^{6} \cdot 4)}$

Rewrite the expression.

$\frac{y^{9}}{y^{6} \cdot 4}$

Step 11

Cancel the common factor of $y^{9}$ and $y^{6}$ .

Factor $y^{6}$ out of $y^{9}$ .

$\frac{y^{6} y^{3}}{y^{6} \cdot 4}$

Cancel the common factors.

Factor $y^{6}$ out of $y^{6} \cdot 4$ .

$\frac{y^{6} y^{3}}{y^{6} (4)}$

Cancel the common factor.

$\frac{y^{6} y^{3}}{y^{6} \cdot 4}$

Rewrite the expression.

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

Simplify ((10x)/(25x^3y^2))÷((32x^7y^4)/(20x^9y^9))

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