Simplify 5x^2y(2x^4y^-3)

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

Step 1

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

Move $x^{4}$ .

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

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

$5 x^{4 + 2} y (2 y^{- 3})$

Add $4$ and $2$ .

$5 x^{6} y (2 y^{- 3})$

Step 2

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

Move $y^{- 3}$ .

$5 x^{6} (y^{- 3} y) \cdot 2$

Multiply $y^{- 3}$ by $y$ .

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

$5 x^{6} (y^{- 3} y^{1}) \cdot 2$

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

$5 x^{6} y^{- 3 + 1} \cdot 2$

Add $- 3$ and $1$ .

$5 x^{6} y^{- 2} \cdot 2$

Step 3

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

$5 x^{6} \frac{1}{y^{2}} \cdot 2$

Step 4

Multiply $5 x^{6} \frac{1}{y^{2}}$ .

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

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

Combine $x^{6}$ and $\frac{5}{y^{2}}$ .

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

Step 5

Move $5$ to the left of $x^{6}$ .

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

Step 6

Multiply $\frac{5 x^{6}}{y^{2}} \cdot 2$ .

Combine $\frac{5 x^{6}}{y^{2}}$ and $2$ .

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

Multiply $2$ by $5$ .

$\frac{10 x^{6}}{y^{2}}$