Basic Math Examples

$\frac{15 c}{4 b} \cdot \frac{2 b^{2} c^{4}}{5 c}$

Step 1

Combine.

$\frac{15 c (2 b^{2} c^{4})}{4 b (5 c)}$

Step 2

Multiply $c$ by $c^{4}$ by adding the exponents.

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Step 2.1

Move $c^{4}$ .

$\frac{15 (c^{4} c) (2 b^{2})}{4 b (5 c)}$

Step 2.2

Multiply $c^{4}$ by $c$ .

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Step 2.2.1

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

$\frac{15 (c^{4} c^{1}) (2 b^{2})}{4 b (5 c)}$

Step 2.2.2

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

$\frac{15 c^{4 + 1} (2 b^{2})}{4 b (5 c)}$

$\frac{15 c^{4 + 1} (2 b^{2})}{4 b (5 c)}$

Step 2.3

Add $4$ and $1$ .

$\frac{15 c^{5} (2 b^{2})}{4 b (5 c)}$

$\frac{15 c^{5} (2 b^{2})}{4 b (5 c)}$

Step 3

Cancel the common factor of $15$ and $5$ .

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Step 3.1

Factor $5$ out of $15 c^{5} (2 b^{2})$ .

$\frac{5 (3 c^{5} (2 b^{2}))}{4 b (5 c)}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $5$ out of $4 b (5 c)$ .

$\frac{5 (3 c^{5} (2 b^{2}))}{5 (4 b (c))}$

Step 3.2.2

Cancel the common factor.

$\frac{5 (3 c^{5} (2 b^{2}))}{5 (4 b (c))}$

Step 3.2.3

Rewrite the expression.

$\frac{3 c^{5} (2 b^{2})}{4 b (c)}$

$\frac{3 c^{5} (2 b^{2})}{4 b (c)}$

$\frac{3 c^{5} (2 b^{2})}{4 b (c)}$

Step 4

Cancel the common factor of $c^{5}$ and $c$ .

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Step 4.1

Factor $c$ out of $3 c^{5} (2 b^{2})$ .

$\frac{c (3 c^{4} (2 b^{2}))}{4 b (c)}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $c$ out of $4 b (c)$ .

$\frac{c (3 c^{4} (2 b^{2}))}{c (4 b)}$

Step 4.2.2

Cancel the common factor.

$\frac{c (3 c^{4} (2 b^{2}))}{c (4 b)}$

Step 4.2.3

Rewrite the expression.

$\frac{3 c^{4} (2 b^{2})}{4 b}$

$\frac{3 c^{4} (2 b^{2})}{4 b}$

$\frac{3 c^{4} (2 b^{2})}{4 b}$

Step 5

Cancel the common factor of $2$ and $4$ .

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Step 5.1

Factor $2$ out of $3 c^{4} (2 b^{2})$ .

$\frac{2 (3 c^{4} (b^{2}))}{4 b}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $4 b$ .

$\frac{2 (3 c^{4} (b^{2}))}{2 (2 b)}$

Step 5.2.2

Cancel the common factor.

$\frac{2 (3 c^{4} (b^{2}))}{2 (2 b)}$

Step 5.2.3

Rewrite the expression.

$\frac{3 c^{4} (b^{2})}{2 b}$

$\frac{3 c^{4} (b^{2})}{2 b}$

$\frac{3 c^{4} (b^{2})}{2 b}$

Step 6

Cancel the common factor of $b^{2}$ and $b$ .

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Step 6.1

Factor $b$ out of $3 c^{4} (b^{2})$ .

$\frac{b (3 c^{4} (b))}{2 b}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $b$ out of $2 b$ .

$\frac{b (3 c^{4} (b))}{b \cdot 2}$

Step 6.2.2

Cancel the common factor.

$\frac{b (3 c^{4} (b))}{b \cdot 2}$

Step 6.2.3

Rewrite the expression.

$\frac{3 c^{4} (b)}{2}$

$\frac{3 c^{4} (b)}{2}$

$\frac{3 c^{4} b}{2}$

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