Pre-Algebra Examples

$\frac{d^{6}}{3 a} \div \frac{d^{2}}{9 a^{2}} \cdot \frac{a}{4 d^{3}}$

Step 1

Combine fractions.

Tap for more steps...

Step 1.1

Combine.

$\frac{\frac{d^{6}}{3 a} a}{\frac{d^{2}}{9 a^{2}} (4 d^{3})}$

Step 1.2

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

$\frac{\frac{d^{6} a}{3 a}}{\frac{d^{2}}{9 a^{2}} (4 d^{3})}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Combine $4$ and $\frac{d^{2}}{9 a^{2}}$ .

$\frac{\frac{d^{6} a}{3 a}}{\frac{4 d^{2}}{9 a^{2}} d^{3}}$

Step 2.2

Combine $\frac{4 d^{2}}{9 a^{2}}$ and $d^{3}$ .

$\frac{\frac{d^{6} a}{3 a}}{\frac{4 d^{2} d^{3}}{9 a^{2}}}$

Step 3

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

Tap for more steps...

Step 3.1

Move $d^{3}$ .

$\frac{\frac{d^{6} a}{3 a}}{\frac{4 (d^{3} d^{2})}{9 a^{2}}}$

Step 3.2

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

$\frac{\frac{d^{6} a}{3 a}}{\frac{4 d^{3 + 2}}{9 a^{2}}}$

Step 3.3

Add $3$ and $2$ .

$\frac{\frac{d^{6} a}{3 a}}{\frac{4 d^{5}}{9 a^{2}}}$

Step 4

Reduce the expression $\frac{d^{6} a}{3 a}$ by cancelling the common factors.

Tap for more steps...

Step 4.1

Cancel the common factor.

$\frac{\frac{d^{6} a}{3 a}}{\frac{4 d^{5}}{9 a^{2}}}$

Step 4.2

Rewrite the expression.

$\frac{\frac{d^{6}}{3}}{\frac{4 d^{5}}{9 a^{2}}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{d^{6}}{3} \cdot \frac{9 a^{2}}{4 d^{5}}$

Step 6

Combine.

$\frac{d^{6} (9 a^{2})}{3 (4 d^{5})}$

Step 7

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

Tap for more steps...

Step 7.1

Factor $d^{5}$ out of $d^{6} (9 a^{2})$ .

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

Step 7.2

Cancel the common factors.

Tap for more steps...

Step 7.2.1

Factor $d^{5}$ out of $3 (4 d^{5})$ .

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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

Step 8

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

Tap for more steps...

Step 8.1

Factor $3$ out of $d (9 a^{2})$ .

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

Step 8.2

Cancel the common factors.

Tap for more steps...

Step 8.2.1

Factor $3$ out of $3 \cdot (4)$ .

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

Step 8.2.2

Cancel the common factor.

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

Step 8.2.3

Rewrite the expression.

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

Step 9

Move $3$ to the left of $d$ .

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