Algebra Examples

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

Step 1

Combine.

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

Step 2

Multiply $x$ by $x^{10}$ by adding the exponents.

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Step 2.1

Move $x^{10}$ .

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

Step 2.2

Multiply $x^{10}$ by $x$ .

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Step 2.2.1

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

$\frac{5 x^{- 2} (2 y^{3})}{3 (x^{10} x^{1})}$

Step 2.2.2

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

$\frac{5 x^{- 2} (2 y^{3})}{3 x^{10 + 1}}$

Step 2.3

Add $10$ and $1$ .

$\frac{5 x^{- 2} (2 y^{3})}{3 x^{11}}$

Step 3

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

$\frac{5 (2 y^{3})}{3 x^{11} x^{2}}$

Step 4

Multiply $x^{11}$ by $x^{2}$ by adding the exponents.

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Step 4.1

Move $x^{2}$ .

$\frac{5 (2 y^{3})}{3 (x^{2} x^{11})}$

Step 4.2

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

$\frac{5 (2 y^{3})}{3 x^{2 + 11}}$

Step 4.3

Add $2$ and $11$ .

$\frac{5 (2 y^{3})}{3 x^{13}}$

Step 5

Multiply $5$ by $2$ .

$\frac{10 y^{3}}{3 x^{13}}$