Algebra Examples

$\frac{4 x}{5} \div \frac{6}{5 x^{3}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{4 x}{5} \cdot \frac{5 x^{3}}{6}$

Step 2

Combine.

$\frac{4 x (5 x^{3})}{5 \cdot 6}$

Step 3

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

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Step 3.1

Move $x^{3}$ .

$\frac{4 (x^{3} x) \cdot 5}{5 \cdot 6}$

Step 3.2

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

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Step 3.2.1

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

$\frac{4 (x^{3} x^{1}) \cdot 5}{5 \cdot 6}$

Step 3.2.2

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

$\frac{4 x^{3 + 1} \cdot 5}{5 \cdot 6}$

Step 3.3

Add $3$ and $1$ .

$\frac{4 x^{4} \cdot 5}{5 \cdot 6}$

Step 4

Cancel the common factor of $4$ and $6$ .

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Step 4.1

Factor $2$ out of $4 x^{4} \cdot 5$ .

$\frac{2 (2 x^{4} \cdot 5)}{5 \cdot 6}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $5 \cdot 6$ .

$\frac{2 (2 x^{4} \cdot 5)}{2 (5 \cdot 3)}$

Step 4.2.2

Cancel the common factor.

$\frac{2 (2 x^{4} \cdot 5)}{2 (5 \cdot 3)}$

Step 4.2.3

Rewrite the expression.

$\frac{2 x^{4} \cdot 5}{5 \cdot 3}$

Step 5

Cancel the common factor of $5$ .

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Step 5.1

Cancel the common factor.

$\frac{2 x^{4} \cdot 5}{5 \cdot 3}$

Step 5.2

Rewrite the expression.

$\frac{2 x^{4}}{3}$