Basic Math Examples

$\frac{d^{7}}{5 a} \div \frac{d^{2}}{10 a^{2}} \cdot \frac{a}{3 d^{3}}$

Step 1

Combine fractions.

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Step 1.1

Combine.

$\frac{\frac{d^{7}}{5 a} a}{\frac{d^{2}}{10 a^{2}} (3 d^{3})}$

Step 1.2

Combine $\frac{d^{7}}{5 a}$ and $a$ .

$\frac{\frac{d^{7} a}{5 a}}{\frac{d^{2}}{10 a^{2}} (3 d^{3})}$

Step 2

Simplify the denominator.

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Step 2.1

Combine $3$ and $\frac{d^{2}}{10 a^{2}}$ .

$\frac{\frac{d^{7} a}{5 a}}{\frac{3 d^{2}}{10 a^{2}} d^{3}}$

Step 2.2

Combine $\frac{3 d^{2}}{10 a^{2}}$ and $d^{3}$ .

$\frac{\frac{d^{7} a}{5 a}}{\frac{3 d^{2} d^{3}}{10 a^{2}}}$

Step 3

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

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Step 3.1

Move $d^{3}$ .

$\frac{\frac{d^{7} a}{5 a}}{\frac{3 (d^{3} d^{2})}{10 a^{2}}}$

Step 3.2

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

$\frac{\frac{d^{7} a}{5 a}}{\frac{3 d^{3 + 2}}{10 a^{2}}}$

Step 3.3

Add $3$ and $2$ .

$\frac{\frac{d^{7} a}{5 a}}{\frac{3 d^{5}}{10 a^{2}}}$

Step 4

Reduce the expression $\frac{d^{7} a}{5 a}$ by cancelling the common factors.

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Step 4.1

Cancel the common factor.

$\frac{\frac{d^{7} a}{5 a}}{\frac{3 d^{5}}{10 a^{2}}}$

Step 4.2

Rewrite the expression.

$\frac{\frac{d^{7}}{5}}{\frac{3 d^{5}}{10 a^{2}}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{d^{7}}{5} \cdot \frac{10 a^{2}}{3 d^{5}}$

Step 6

Combine.

$\frac{d^{7} (10 a^{2})}{5 (3 d^{5})}$

Step 7

Cancel the common factor of $d^{7}$ and $d^{5}$ .

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Step 7.1

Factor $d^{5}$ out of $d^{7} (10 a^{2})$ .

$\frac{d^{5} (d^{2} (10 a^{2}))}{5 (3 d^{5})}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $d^{5}$ out of $5 (3 d^{5})$ .

$\frac{d^{5} (d^{2} (10 a^{2}))}{d^{5} (5 \cdot (3))}$

Step 7.2.2

Cancel the common factor.

$\frac{d^{5} (d^{2} (10 a^{2}))}{d^{5} (5 \cdot (3))}$

Step 7.2.3

Rewrite the expression.

$\frac{d^{2} (10 a^{2})}{5 \cdot (3)}$

Step 8

Cancel the common factor of $10$ and $5$ .

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Step 8.1

Factor $5$ out of $d^{2} (10 a^{2})$ .

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

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $5$ out of $5 \cdot (3)$ .

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

Step 8.2.2

Cancel the common factor.

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

Step 8.2.3

Rewrite the expression.

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

Step 9

Move $2$ to the left of $d^{2}$ .

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