Simplify (2x^4)/(10y^-2)*(5y^3)/(4x^3)

$\frac{2 x^{4}}{10 y^{- 2}} \cdot \frac{5 y^{3}}{4 x^{3}}$

Step 1

Combine.

$\frac{2 x^{4} (5 y^{3})}{10 y^{- 2} (4 x^{3})}$

Step 2

Move $y^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{2 x^{4} (5 y^{3}) y^{2}}{10 (4 x^{3})}$

Step 3

Multiply $y^{3}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$\frac{2 x^{4} (5 (y^{2} y^{3}))}{10 (4 x^{3})}$

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

$\frac{2 x^{4} (5 y^{2 + 3})}{10 (4 x^{3})}$

Add $2$ and $3$ .

$\frac{2 x^{4} (5 y^{5})}{10 (4 x^{3})}$

Step 4

Cancel the common factor of $2$ and $10$ .

Factor $2$ out of $2 x^{4} (5 y^{5})$ .

$\frac{2 (x^{4} (5 y^{5}))}{10 (4 x^{3})}$

Cancel the common factors.

Factor $2$ out of $10 (4 x^{3})$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

Cancel the common factor of $x^{4}$ and $x^{3}$ .

Factor $x^{3}$ out of $x^{4} (5 y^{5})$ .

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

Cancel the common factors.

Factor $x^{3}$ out of $5 (4 x^{3})$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 6

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

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

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