Simplify 2x^3y^-2*2x^5

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

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

Move $x^{5}$ .

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

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

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

Add $5$ and $3$ .

$2 x^{8} y^{- 2} \cdot 2$

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

$2 x^{8} \frac{1}{y^{2}} \cdot 2$

Multiply $2 x^{8} \frac{1}{y^{2}}$ .

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

$x^{8} \frac{2}{y^{2}} \cdot 2$

Combine $x^{8}$ and $\frac{2}{y^{2}}$ .

$\frac{x^{8} \cdot 2}{y^{2}} \cdot 2$

Move $2$ to the left of $x^{8}$ .

$\frac{2 \cdot x^{8}}{y^{2}} \cdot 2$

Multiply $\frac{2 x^{8}}{y^{2}} \cdot 2$ .

Combine $\frac{2 x^{8}}{y^{2}}$ and $2$ .

$\frac{2 x^{8} \cdot 2}{y^{2}}$

Multiply $2$ by $2$ .

$\frac{4 x^{8}}{y^{2}}$