Basic Math Examples

$\frac{15 b}{8 y} \cdot \frac{3 b y}{2 y^{5}}$

Step 1

Combine.

$\frac{15 b (3 b y)}{8 y (2 y^{5})}$

Step 2

Multiply $b$ by $b$ by adding the exponents.

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Step 2.1

Move $b$ .

$\frac{15 (b \cdot b) (3 y)}{8 y (2 y^{5})}$

Step 2.2

Multiply $b$ by $b$ .

$\frac{15 b^{2} (3 y)}{8 y (2 y^{5})}$

Step 3

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

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Step 3.1

Move $y^{5}$ .

$\frac{15 b^{2} (3 y)}{8 (y^{5} y) \cdot 2}$

Step 3.2

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

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Step 3.2.1

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

$\frac{15 b^{2} (3 y)}{8 (y^{5} y^{1}) \cdot 2}$

Step 3.2.2

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

$\frac{15 b^{2} (3 y)}{8 y^{5 + 1} \cdot 2}$

Step 3.3

Add $5$ and $1$ .

$\frac{15 b^{2} (3 y)}{8 y^{6} \cdot 2}$

Step 4

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

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Step 4.1

Factor $y$ out of $15 b^{2} (3 y)$ .

$\frac{y (15 b^{2} \cdot (3))}{8 y^{6} \cdot 2}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $y$ out of $8 y^{6} \cdot 2$ .

$\frac{y (15 b^{2} \cdot (3))}{y (8 y^{5} \cdot 2)}$

Step 4.2.2

Cancel the common factor.

$\frac{y (15 b^{2} \cdot (3))}{y (8 y^{5} \cdot 2)}$

Step 4.2.3

Rewrite the expression.

$\frac{15 b^{2} \cdot (3)}{8 y^{5} \cdot 2}$

Step 5

Multiply.

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Step 5.1

Multiply $3$ by $15$ .

$\frac{45 b^{2}}{8 y^{5} \cdot 2}$

Step 5.2

Multiply $2$ by $8$ .

$\frac{45 b^{2}}{16 y^{5}}$