Algebra Examples

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

Step 1

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

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Step 1.1

Move $x^{5}$ .

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

Step 1.2

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

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

Step 1.3

Add $5$ and $3$ .

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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

Step 4

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

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Multiply $2$ by $2$ .

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