Simplify ((d^7)/(5a))÷((d^2)/(10a^2))*a/(3d^3)

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

Step 1

Combine fractions.

Combine.

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

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.

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

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

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.

Move $d^{3}$ .

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

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

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

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.

Cancel the common factor.

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

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 $d^{5}$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 8

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 9

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

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

Simplify ((d^7)/(5a))÷((d^2)/(10a^2))*a/(3d^3)

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