Basic Math Examples

$\frac{d^{5}}{3 a} \div \frac{d^{2}}{6 a^{2}} \cdot \frac{a}{4 d^{3}}$

Step 1

Combine fractions.

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Step 1.1

Combine.

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

Step 1.2

Combine $\frac{d^{5}}{3 a}$ and $a$ .

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

Step 2

Simplify the denominator.

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Step 2.1

Combine $4$ and $\frac{d^{2}}{6 a^{2}}$ .

$\frac{\frac{d^{5} a}{3 a}}{\frac{4 d^{2}}{6 a^{2}} d^{3}}$

Step 2.2

Combine $\frac{4 d^{2}}{6 a^{2}}$ and $d^{3}$ .

$\frac{\frac{d^{5} a}{3 a}}{\frac{4 d^{2} d^{3}}{6 a^{2}}}$

Step 3

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

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Step 3.1

Move $d^{3}$ .

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

Step 3.2

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

$\frac{\frac{d^{5} a}{3 a}}{\frac{4 d^{3 + 2}}{6 a^{2}}}$

Step 3.3

Add $3$ and $2$ .

$\frac{\frac{d^{5} a}{3 a}}{\frac{4 d^{5}}{6 a^{2}}}$

Step 4

Reduce the expression $\frac{d^{5} a}{3 a}$ by cancelling the common factors.

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Step 4.1

Cancel the common factor.

$\frac{\frac{d^{5} a}{3 a}}{\frac{4 d^{5}}{6 a^{2}}}$

Step 4.2

Rewrite the expression.

$\frac{\frac{d^{5}}{3}}{\frac{4 d^{5}}{6 a^{2}}}$

Step 5

Reduce the expression $\frac{4 d^{5}}{6 a^{2}}$ by cancelling the common factors.

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Step 5.1

Factor $2$ out of $4 d^{5}$ .

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

Step 5.2

Factor $2$ out of $6 a^{2}$ .

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

Step 5.3

Cancel the common factor.

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

Step 5.4

Rewrite the expression.

$\frac{\frac{d^{5}}{3}}{\frac{2 d^{5}}{3 a^{2}}}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

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

Step 7

Combine.

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

Step 8

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

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Step 8.1

Cancel the common factor.

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

Step 8.2

Rewrite the expression.

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

Step 9

Cancel the common factor of $3$ .

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Step 9.1

Cancel the common factor.

$\frac{3 a^{2}}{3 \cdot 2}$

Step 9.2

Rewrite the expression.

$\frac{a^{2}}{2}$