Basic Math Examples

${(3 d)}^{6} \div (- \frac{1}{2} d^{2}) \div 12 d^{3}$

Step 1

Rewrite the division as a fraction.

$\frac{{(3 d)}^{6} \div (- \frac{1}{2} d^{2})}{12 d^{3}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

${(3 d)}^{6} \div (- \frac{1}{2} d^{2}) \cdot \frac{1}{12 d^{3}}$

Step 3

Combine.

$\frac{{(3 d)}^{6} \cdot 1}{- \frac{1}{2} d^{2} (12 d^{3})}$

Step 4

Multiply $d^{2}$ by $d^{3}$ by adding the exponents.

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Step 4.1

Move $d^{3}$ .

$\frac{{(3 d)}^{6} \cdot 1}{- \frac{1}{2} (d^{3} d^{2}) \cdot 12}$

Step 4.2

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

$\frac{{(3 d)}^{6} \cdot 1}{- \frac{1}{2} d^{3 + 2} \cdot 12}$

Step 4.3

Add $3$ and $2$ .

$\frac{{(3 d)}^{6} \cdot 1}{- \frac{1}{2} d^{5} \cdot 12}$

Step 5

Multiply ${(3 d)}^{6}$ by $1$ .

$\frac{{(3 d)}^{6}}{- \frac{1}{2} d^{5} \cdot 12}$

Step 6

Simplify the numerator.

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Step 6.1

Apply the product rule to $3 d$ .

$\frac{3^{6} d^{6}}{- \frac{1}{2} d^{5} \cdot 12}$

Step 6.2

Raise $3$ to the power of $6$ .

$\frac{729 d^{6}}{- \frac{1}{2} d^{5} \cdot 12}$

Step 7

Simplify the denominator.

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Step 7.1

Multiply $12$ by $- 1$ .

$\frac{729 d^{6}}{- 12 (\frac{1}{2}) d^{5}}$

Step 7.2

Combine $- 12$ and $\frac{1}{2}$ .

$\frac{729 d^{6}}{\frac{- 12}{2} d^{5}}$

Step 7.3

Combine $\frac{- 12}{2}$ and $d^{5}$ .

$\frac{729 d^{6}}{\frac{- 12 d^{5}}{2}}$

Step 8

Reduce the expression by cancelling the common factors.

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Step 8.1

Reduce the expression $\frac{- 12 d^{5}}{2}$ by cancelling the common factors.

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Step 8.1.1

Factor $2$ out of $- 12 d^{5}$ .

$\frac{729 d^{6}}{\frac{2 (- 6 d^{5})}{2}}$

Step 8.1.2

Factor $2$ out of $2$ .

$\frac{729 d^{6}}{\frac{2 (- 6 d^{5})}{2 (1)}}$

Step 8.1.3

Cancel the common factor.

$\frac{729 d^{6}}{\frac{2 (- 6 d^{5})}{2 \cdot 1}}$

Step 8.1.4

Rewrite the expression.

$\frac{729 d^{6}}{\frac{- 6 d^{5}}{1}}$

Step 8.2

Divide $- 6 d^{5}$ by $1$ .

$\frac{729 d^{6}}{- 6 d^{5}}$

Step 9

Cancel the common factor of $729$ and $- 6$ .

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Step 9.1

Factor $3$ out of $729 d^{6}$ .

$\frac{3 (243 d^{6})}{- 6 d^{5}}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $3$ out of $- 6 d^{5}$ .

$\frac{3 (243 d^{6})}{3 (- 2 d^{5})}$

Step 9.2.2

Cancel the common factor.

$\frac{3 (243 d^{6})}{3 (- 2 d^{5})}$

Step 9.2.3

Rewrite the expression.

$\frac{243 d^{6}}{- 2 d^{5}}$

Step 10

Cancel the common factor of $d^{6}$ and $d^{5}$ .

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Step 10.1

Factor $d^{5}$ out of $243 d^{6}$ .

$\frac{d^{5} (243 d)}{- 2 d^{5}}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $d^{5}$ out of $- 2 d^{5}$ .

$\frac{d^{5} (243 d)}{d^{5} \cdot - 2}$

Step 10.2.2

Cancel the common factor.

$\frac{d^{5} (243 d)}{d^{5} \cdot - 2}$

Step 10.2.3

Rewrite the expression.

$\frac{243 d}{- 2}$

Step 11

Move the negative in front of the fraction.

$- \frac{243 d}{2}$