Algebra Examples

$(\frac{9}{20} d^{5}) (2 d^{- 2}) (\frac{4}{3} d^{9})$

Step 1

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

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Step 1.1

Move $d^{- 2}$ .

$\frac{9}{20} (d^{- 2} d^{5}) \cdot 2 (\frac{4}{3} d^{9})$

Step 1.2

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

$\frac{9}{20} d^{- 2 + 5} \cdot 2 (\frac{4}{3} d^{9})$

Step 1.3

Add $- 2$ and $5$ .

$\frac{9}{20} d^{3} \cdot 2 (\frac{4}{3} d^{9})$

Step 2

Multiply $d^{3}$ by $d^{9}$ by adding the exponents.

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Step 2.1

Move $d^{9}$ .

$\frac{9}{20} (d^{9} d^{3}) \cdot 2 \frac{4}{3}$

Step 2.2

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

$\frac{9}{20} d^{9 + 3} \cdot 2 \frac{4}{3}$

Step 2.3

Add $9$ and $3$ .

$\frac{9}{20} d^{12} \cdot 2 \frac{4}{3}$

Step 3

Combine $\frac{9}{20}$ and $d^{12}$ .

$\frac{9 d^{12}}{20} \cdot 2 \frac{4}{3}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Factor $2$ out of $20$ .

$\frac{9 d^{12}}{2 (10)} \cdot 2 \frac{4}{3}$

Step 4.2

Cancel the common factor.

$\frac{9 d^{12}}{2 \cdot 10} \cdot 2 \frac{4}{3}$

Step 4.3

Rewrite the expression.

$\frac{9 d^{12}}{10} \cdot \frac{4}{3}$

Step 5

Combine.

$\frac{9 d^{12} \cdot 4}{10 \cdot 3}$

Step 6

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

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Step 6.1

Factor $3$ out of $9 d^{12} \cdot 4$ .

$\frac{3 (3 d^{12} \cdot 4)}{10 \cdot 3}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $3$ out of $10 \cdot 3$ .

$\frac{3 (3 d^{12} \cdot 4)}{3 \cdot 10}$

Step 6.2.2

Cancel the common factor.

$\frac{3 (3 d^{12} \cdot 4)}{3 \cdot 10}$

Step 6.2.3

Rewrite the expression.

$\frac{3 d^{12} \cdot 4}{10}$

Step 7

Cancel the common factor of $4$ and $10$ .

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Step 7.1

Factor $2$ out of $3 d^{12} \cdot 4$ .

$\frac{2 (3 d^{12} \cdot 2)}{10}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $2$ out of $10$ .

$\frac{2 (3 d^{12} \cdot 2)}{2 (5)}$

Step 7.2.2

Cancel the common factor.

$\frac{2 (3 d^{12} \cdot 2)}{2 \cdot 5}$

Step 7.2.3

Rewrite the expression.

$\frac{3 d^{12} \cdot 2}{5}$

Step 8

Multiply $2$ by $3$ .

$\frac{6 d^{12}}{5}$