Basic Math Examples

$\frac{2 c}{3 b} \cdot \frac{9 b^{2} c^{5}}{4 c}$

Step 1

Combine.

$\frac{2 c (9 b^{2} c^{5})}{3 b (4 c)}$

Step 2

Multiply $c$ by $c^{5}$ by adding the exponents.

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Step 2.1

Move $c^{5}$ .

$\frac{2 (c^{5} c) (9 b^{2})}{3 b (4 c)}$

Step 2.2

Multiply $c^{5}$ by $c$ .

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Step 2.2.1

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

$\frac{2 (c^{5} c^{1}) (9 b^{2})}{3 b (4 c)}$

Step 2.2.2

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

$\frac{2 c^{5 + 1} (9 b^{2})}{3 b (4 c)}$

$\frac{2 c^{5 + 1} (9 b^{2})}{3 b (4 c)}$

Step 2.3

Add $5$ and $1$ .

$\frac{2 c^{6} (9 b^{2})}{3 b (4 c)}$

$\frac{2 c^{6} (9 b^{2})}{3 b (4 c)}$

Step 3

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

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Step 3.1

Factor $2$ out of $2 c^{6} (9 b^{2})$ .

$\frac{2 (c^{6} (9 b^{2}))}{3 b (4 c)}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{2 (c^{6} (9 b^{2}))}{2 (3 b (2 c))}$

Step 3.2.2

Cancel the common factor.

$\frac{2 (c^{6} (9 b^{2}))}{2 (3 b (2 c))}$

Step 3.2.3

Rewrite the expression.

$\frac{c^{6} (9 b^{2})}{3 b (2 c)}$

$\frac{c^{6} (9 b^{2})}{3 b (2 c)}$

$\frac{c^{6} (9 b^{2})}{3 b (2 c)}$

Step 4

Cancel the common factor of $c^{6}$ and $c$ .

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Step 4.1

Factor $c$ out of $c^{6} (9 b^{2})$ .

$\frac{c (c^{5} (9 b^{2}))}{3 b (2 c)}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $c$ out of $3 b (2 c)$ .

$\frac{c (c^{5} (9 b^{2}))}{c (3 b \cdot (2))}$

Step 4.2.2

Cancel the common factor.

$\frac{c (c^{5} (9 b^{2}))}{c (3 b \cdot (2))}$

Step 4.2.3

Rewrite the expression.

$\frac{c^{5} (9 b^{2})}{3 b \cdot (2)}$

$\frac{c^{5} (9 b^{2})}{3 b \cdot (2)}$

$\frac{c^{5} (9 b^{2})}{3 b \cdot (2)}$

Step 5

Cancel the common factor of $9$ and $3$ .

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Step 5.1

Factor $3$ out of $c^{5} (9 b^{2})$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $3$ out of $3 b \cdot (2)$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

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

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

Step 6

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

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Step 6.1

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

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $b$ out of $b \cdot (2)$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

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

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

Step 7

Move $3$ to the left of $c^{5}$ .

$\frac{3 c^{5} b}{2}$

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