Algebra Examples

$\frac{7}{4 x^{3}} \cdot \frac{10 x}{2 x}$

Step 1

Combine.

$\frac{7 (10 x)}{4 x^{3} (2 x)}$

Step 2

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

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Step 2.1

Move $x$ .

$\frac{7 (10 x)}{4 (x \cdot x^{3}) \cdot 2}$

Step 2.2

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

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Step 2.2.1

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

$\frac{7 (10 x)}{4 (x^{1} x^{3}) \cdot 2}$

Step 2.2.2

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

$\frac{7 (10 x)}{4 x^{1 + 3} \cdot 2}$

$\frac{7 (10 x)}{4 x^{1 + 3} \cdot 2}$

Step 2.3

Add $1$ and $3$ .

$\frac{7 (10 x)}{4 x^{4} \cdot 2}$

$\frac{7 (10 x)}{4 x^{4} \cdot 2}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $10$ and $4$ .

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Step 3.1.1

Factor $2$ out of $7 (10 x)$ .

$\frac{2 (7 (5 x))}{4 x^{4} \cdot 2}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

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

$\frac{2 (7 (5 x))}{2 (2 x^{4} \cdot 2)}$

Step 3.1.2.2

Cancel the common factor.

$\frac{2 (7 (5 x))}{2 (2 x^{4} \cdot 2)}$

Step 3.1.2.3

Rewrite the expression.

$\frac{7 (5 x)}{2 x^{4} \cdot 2}$

$\frac{7 (5 x)}{2 x^{4} \cdot 2}$

$\frac{7 (5 x)}{2 x^{4} \cdot 2}$

Step 3.2

Cancel the common factor of $x$ and $x^{4}$ .

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Step 3.2.1

Factor $x$ out of $7 (5 x)$ .

$\frac{x (7 \cdot (5))}{2 x^{4} \cdot 2}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

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

$\frac{x (7 \cdot (5))}{x (2 x^{3} \cdot 2)}$

Step 3.2.2.2

Cancel the common factor.

$\frac{x (7 \cdot (5))}{x (2 x^{3} \cdot 2)}$

Step 3.2.2.3

Rewrite the expression.

$\frac{7 \cdot (5)}{2 x^{3} \cdot 2}$

$\frac{7 \cdot (5)}{2 x^{3} \cdot 2}$

$\frac{7 \cdot (5)}{2 x^{3} \cdot 2}$

$\frac{7 \cdot (5)}{2 x^{3} \cdot 2}$

Step 4

Multiply $7$ by $5$ .

$\frac{35}{2 x^{3} \cdot 2}$

Step 5

Multiply $2$ by $2$ .

$\frac{35}{4 x^{3}}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$