Simplify (32x^3y)/(5xy^2)*(15y)/(8x^2y^4)

$\frac{32 x^{3} y}{5 x y^{2}} \cdot \frac{15 y}{8 x^{2} y^{4}}$

Step 1

Combine.

$\frac{32 x^{3} y (15 y)}{5 x y^{2} (8 x^{2} y^{4})}$

Step 2

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

Move $y$ .

$\frac{32 x^{3} (y \cdot y) \cdot 15}{5 x y^{2} (8 x^{2} y^{4})}$

Multiply $y$ by $y$ .

$\frac{32 x^{3} y^{2} \cdot 15}{5 x y^{2} (8 x^{2} y^{4})}$

Step 3

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

Move $x^{2}$ .

$\frac{32 x^{3} y^{2} \cdot 15}{5 (x^{2} x) y^{2} (8 y^{4})}$

Multiply $x^{2}$ by $x$ .

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

$\frac{32 x^{3} y^{2} \cdot 15}{5 (x^{2} x^{1}) y^{2} (8 y^{4})}$

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

$\frac{32 x^{3} y^{2} \cdot 15}{5 x^{2 + 1} y^{2} (8 y^{4})}$

Add $2$ and $1$ .

$\frac{32 x^{3} y^{2} \cdot 15}{5 x^{3} y^{2} (8 y^{4})}$

Step 4

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

Move $y^{4}$ .

$\frac{32 x^{3} y^{2} \cdot 15}{5 x^{3} (y^{4} y^{2}) \cdot 8}$

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

$\frac{32 x^{3} y^{2} \cdot 15}{5 x^{3} y^{4 + 2} \cdot 8}$

Add $4$ and $2$ .

$\frac{32 x^{3} y^{2} \cdot 15}{5 x^{3} y^{6} \cdot 8}$

Step 5

Cancel the common factor of $32$ and $8$ .

Factor $8$ out of $32 x^{3} y^{2} \cdot 15$ .

$\frac{8 (4 x^{3} y^{2} \cdot 15)}{5 x^{3} y^{6} \cdot 8}$

Cancel the common factors.

Factor $8$ out of $5 x^{3} y^{6} \cdot 8$ .

$\frac{8 (4 x^{3} y^{2} \cdot 15)}{8 \cdot (5 x^{3} y^{6})}$

Cancel the common factor.

$\frac{8 (4 x^{3} y^{2} \cdot 15)}{8 \cdot (5 x^{3} y^{6})}$

Rewrite the expression.

$\frac{4 x^{3} y^{2} \cdot 15}{5 x^{3} y^{6}}$

Step 6

Cancel the common factor of $x^{3}$ .

Cancel the common factor.

$\frac{4 x^{3} y^{2} \cdot 15}{5 x^{3} y^{6}}$

Rewrite the expression.

$\frac{4 y^{2} \cdot 15}{5 y^{6}}$

Step 7

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

Factor $y^{2}$ out of $4 y^{2} \cdot 15$ .

$\frac{y^{2} (4 \cdot 15)}{5 y^{6}}$

Cancel the common factors.

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

$\frac{y^{2} (4 \cdot 15)}{y^{2} (5 y^{4})}$

Cancel the common factor.

$\frac{y^{2} (4 \cdot 15)}{y^{2} (5 y^{4})}$

Rewrite the expression.

$\frac{4 \cdot 15}{5 y^{4}}$

Step 8

Cancel the common factor of $15$ and $5$ .

Factor $5$ out of $4 \cdot 15$ .

$\frac{5 (4 \cdot 3)}{5 y^{4}}$

Cancel the common factors.

Factor $5$ out of $5 y^{4}$ .

$\frac{5 (4 \cdot 3)}{5 (y^{4})}$

Cancel the common factor.

$\frac{5 (4 \cdot 3)}{5 y^{4}}$

Rewrite the expression.

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

Step 9

Multiply $4$ by $3$ .

$\frac{12}{y^{4}}$

Simplify (32x^3y)/(5xy^2)*(15y)/(8x^2y^4)

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