Simplify (5x^3y^-5)(4xy^3)

$(5 x^{3} y^{- 5}) (4 x y^{3})$

Step 1

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

Move $x$ .

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

Multiply $x$ by $x^{3}$ .

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

$5 (x^{1} x^{3}) y^{- 5} (4 y^{3})$

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

$5 x^{1 + 3} y^{- 5} (4 y^{3})$

Add $1$ and $3$ .

$5 x^{4} y^{- 5} (4 y^{3})$

Step 2

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

Move $y^{3}$ .

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

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

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

Subtract $5$ from $3$ .

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

Step 3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$5 x^{4} \frac{1}{y^{2}} \cdot 4$

Step 4

Multiply $5 x^{4} \frac{1}{y^{2}}$ .

Combine $5$ and $\frac{1}{y^{2}}$ .

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

Combine $x^{4}$ and $\frac{5}{y^{2}}$ .

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

Step 5

Move $5$ to the left of $x^{4}$ .

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

Step 6

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

Combine $\frac{5 x^{4}}{y^{2}}$ and $4$ .

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

Multiply $4$ by $5$ .

$\frac{20 x^{4}}{y^{2}}$