Simplify (80x^4)/(y^3)*(xy)/(5x^2)

$\frac{80 x^{4}}{y^{3}} \cdot \frac{x y}{5 x^{2}}$

Step 1

Combine.

$\frac{80 x^{4} (x y)}{y^{3} (5 x^{2})}$

Step 2

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

Move $x$ .

$\frac{80 (x \cdot x^{4}) y}{y^{3} (5 x^{2})}$

Multiply $x$ by $x^{4}$ .

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

$\frac{80 (x^{1} x^{4}) y}{y^{3} (5 x^{2})}$

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

$\frac{80 x^{1 + 4} y}{y^{3} (5 x^{2})}$

$\frac{80 x^{1 + 4} y}{y^{3} (5 x^{2})}$

Add $1$ and $4$ .

$\frac{80 x^{5} y}{y^{3} (5 x^{2})}$

$\frac{80 x^{5} y}{y^{3} (5 x^{2})}$

Step 3

Cancel the common factor of $80$ and $5$ .

Factor $5$ out of $80 x^{5} y$ .

$\frac{5 (16 x^{5} y)}{y^{3} (5 x^{2})}$

Cancel the common factors.

Factor $5$ out of $y^{3} (5 x^{2})$ .

$\frac{5 (16 x^{5} y)}{5 (y^{3} (x^{2}))}$

Cancel the common factor.

$\frac{5 (16 x^{5} y)}{5 (y^{3} (x^{2}))}$

Rewrite the expression.

$\frac{16 x^{5} y}{y^{3} (x^{2})}$

$\frac{16 x^{5} y}{y^{3} (x^{2})}$

$\frac{16 x^{5} y}{y^{3} (x^{2})}$

Step 4

Cancel the common factor of $x^{5}$ and $x^{2}$ .

Factor $x^{2}$ out of $16 x^{5} y$ .

$\frac{x^{2} (16 x^{3} y)}{y^{3} (x^{2})}$

Cancel the common factors.

Factor $x^{2}$ out of $y^{3} (x^{2})$ .

$\frac{x^{2} (16 x^{3} y)}{x^{2} y^{3}}$

Cancel the common factor.

$\frac{x^{2} (16 x^{3} y)}{x^{2} y^{3}}$

Rewrite the expression.

$\frac{16 x^{3} y}{y^{3}}$

$\frac{16 x^{3} y}{y^{3}}$

$\frac{16 x^{3} y}{y^{3}}$

Step 5

Cancel the common factor of $y$ and $y^{3}$ .

Factor $y$ out of $16 x^{3} y$ .

$\frac{y (16 x^{3})}{y^{3}}$

Cancel the common factors.

Factor $y$ out of $y^{3}$ .

$\frac{y (16 x^{3})}{y \cdot y^{2}}$

Cancel the common factor.

$\frac{y (16 x^{3})}{y \cdot y^{2}}$

Rewrite the expression.

$\frac{16 x^{3}}{y^{2}}$

$\frac{16 x^{3}}{y^{2}}$

$\frac{16 x^{3}}{y^{2}}$

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