Algebra Examples

$(- \frac{3}{4} b^{2}) (- 6 a^{2} b^{5})$

Step 1

Multiply $b^{2}$ by $b^{5}$ by adding the exponents.

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Step 1.1

Move $b^{5}$ .

$- \frac{3}{4} (b^{5} b^{2}) (- 6 a^{2})$

Step 1.2

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

$- \frac{3}{4} b^{5 + 2} (- 6 a^{2})$

Step 1.3

Add $5$ and $2$ .

$- \frac{3}{4} b^{7} (- 6 a^{2})$

Step 2

Rewrite using the commutative property of multiplication.

$- \frac{3}{4} \cdot - 6 b^{7} a^{2}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{- 3}{4} \cdot - 6 b^{7} a^{2}$

Step 3.2

Factor $2$ out of $4$ .

$\frac{- 3}{2 (2)} \cdot - 6 b^{7} a^{2}$

Step 3.3

Factor $2$ out of $- 6$ .

$\frac{- 3}{2 \cdot 2} \cdot (2 \cdot - 3) b^{7} a^{2}$

Step 3.4

Cancel the common factor.

$\frac{- 3}{2 \cdot 2} \cdot (2 \cdot - 3) b^{7} a^{2}$

Step 3.5

Rewrite the expression.

$\frac{- 3}{2} \cdot - 3 b^{7} a^{2}$

Step 4

Combine $\frac{- 3}{2}$ and $- 3$ .

$\frac{- 3 \cdot - 3}{2} b^{7} a^{2}$

Step 5

Multiply $- 3$ by $- 3$ .

$\frac{9}{2} b^{7} a^{2}$

Step 6

Combine $\frac{9}{2}$ and $b^{7}$ .

$\frac{9 b^{7}}{2} a^{2}$

Step 7

Combine $\frac{9 b^{7}}{2}$ and $a^{2}$ .

$\frac{9 b^{7} a^{2}}{2}$