Basic Math Examples

$\frac{15 a^{2} c}{8 b} \cdot \frac{24 b^{2} c}{5 a}$

Step 1

Combine.

$\frac{15 a^{2} c (24 b^{2} c)}{8 b (5 a)}$

Step 2

Multiply $c$ by $c$ by adding the exponents.

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Step 2.1

Move $c$ .

$\frac{15 a^{2} (c \cdot c) (24 b^{2})}{8 b (5 a)}$

Step 2.2

Multiply $c$ by $c$ .

$\frac{15 a^{2} c^{2} (24 b^{2})}{8 b (5 a)}$

$\frac{15 a^{2} c^{2} (24 b^{2})}{8 b (5 a)}$

Step 3

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

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Step 3.1

Factor $5$ out of $15 a^{2} c^{2} (24 b^{2})$ .

$\frac{5 (3 a^{2} c^{2} (24 b^{2}))}{8 b (5 a)}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $5$ out of $8 b (5 a)$ .

$\frac{5 (3 a^{2} c^{2} (24 b^{2}))}{5 (8 b (a))}$

Step 3.2.2

Cancel the common factor.

$\frac{5 (3 a^{2} c^{2} (24 b^{2}))}{5 (8 b (a))}$

Step 3.2.3

Rewrite the expression.

$\frac{3 a^{2} c^{2} (24 b^{2})}{8 b (a)}$

$\frac{3 a^{2} c^{2} (24 b^{2})}{8 b (a)}$

$\frac{3 a^{2} c^{2} (24 b^{2})}{8 b (a)}$

Step 4

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

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Step 4.1

Factor $a$ out of $3 a^{2} c^{2} (24 b^{2})$ .

$\frac{a (3 a c^{2} (24 b^{2}))}{8 b (a)}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $a$ out of $8 b (a)$ .

$\frac{a (3 a c^{2} (24 b^{2}))}{a (8 b)}$

Step 4.2.2

Cancel the common factor.

$\frac{a (3 a c^{2} (24 b^{2}))}{a (8 b)}$

Step 4.2.3

Rewrite the expression.

$\frac{3 a c^{2} (24 b^{2})}{8 b}$

$\frac{3 a c^{2} (24 b^{2})}{8 b}$

$\frac{3 a c^{2} (24 b^{2})}{8 b}$

Step 5

Cancel the common factor of $24$ and $8$ .

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Step 5.1

Factor $8$ out of $3 a c^{2} (24 b^{2})$ .

$\frac{8 (3 a c^{2} (3 b^{2}))}{8 b}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $8$ out of $8 b$ .

$\frac{8 (3 a c^{2} (3 b^{2}))}{8 (b)}$

Step 5.2.2

Cancel the common factor.

$\frac{8 (3 a c^{2} (3 b^{2}))}{8 b}$

Step 5.2.3

Rewrite the expression.

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

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

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

Step 6

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

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Step 6.1

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

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

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

$\frac{b (3 a c^{2} (3 b))}{b^{1}}$

Step 6.2.2

Factor $b$ out of $b^{1}$ .

$\frac{b (3 a c^{2} (3 b))}{b \cdot 1}$

Step 6.2.3

Cancel the common factor.

$\frac{b (3 a c^{2} (3 b))}{b \cdot 1}$

Step 6.2.4

Rewrite the expression.

$\frac{3 a c^{2} (3 b)}{1}$

Step 6.2.5

Divide $3 a c^{2} (3 b)$ by $1$ .

$3 a c^{2} (3 b)$

$3 a c^{2} (3 b)$

$3 a c^{2} (3 b)$

Step 7

Multiply $3$ by $3$ .

$9 a c^{2} b$

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