Simplify ((10rs^3)/(2s^4))÷((2s^4)/(10r^2s^2))

$\frac{10 r s^{3}}{2 s^{4}} \div \frac{2 s^{4}}{10 r^{2} s^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{10 r s^{3}}{2 s^{4}} \cdot \frac{10 r^{2} s^{2}}{2 s^{4}}$

Step 2

Combine.

$\frac{10 r s^{3} (10 r^{2} s^{2})}{2 s^{4} (2 s^{4})}$

Step 3

Multiply $r$ by $r^{2}$ by adding the exponents.

Move $r^{2}$ .

$\frac{10 (r^{2} r) s^{3} (10 s^{2})}{2 s^{4} (2 s^{4})}$

Multiply $r^{2}$ by $r$ .

Raise $r$ to the power of $1$ .

$\frac{10 (r^{2} r^{1}) s^{3} (10 s^{2})}{2 s^{4} (2 s^{4})}$

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

$\frac{10 r^{2 + 1} s^{3} (10 s^{2})}{2 s^{4} (2 s^{4})}$

Add $2$ and $1$ .

$\frac{10 r^{3} s^{3} (10 s^{2})}{2 s^{4} (2 s^{4})}$

Step 4

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

Move $s^{2}$ .

$\frac{10 r^{3} (s^{2} s^{3}) \cdot 10}{2 s^{4} (2 s^{4})}$

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

$\frac{10 r^{3} s^{2 + 3} \cdot 10}{2 s^{4} (2 s^{4})}$

Add $2$ and $3$ .

$\frac{10 r^{3} s^{5} \cdot 10}{2 s^{4} (2 s^{4})}$

Step 5

Multiply $s^{4}$ by $s^{4}$ by adding the exponents.

Move $s^{4}$ .

$\frac{10 r^{3} s^{5} \cdot 10}{2 (s^{4} s^{4}) \cdot 2}$

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

$\frac{10 r^{3} s^{5} \cdot 10}{2 s^{4 + 4} \cdot 2}$

Add $4$ and $4$ .

$\frac{10 r^{3} s^{5} \cdot 10}{2 s^{8} \cdot 2}$

Step 6

Cancel the common factor of $10$ and $2$ .

Factor $2$ out of $10 r^{3} s^{5} \cdot 10$ .

$\frac{2 (5 r^{3} s^{5} \cdot 10)}{2 s^{8} \cdot 2}$

Cancel the common factors.

Factor $2$ out of $2 s^{8} \cdot 2$ .

$\frac{2 (5 r^{3} s^{5} \cdot 10)}{2 (s^{8} \cdot 2)}$

Cancel the common factor.

$\frac{2 (5 r^{3} s^{5} \cdot 10)}{2 (s^{8} \cdot 2)}$

Rewrite the expression.

$\frac{5 r^{3} s^{5} \cdot 10}{s^{8} \cdot 2}$

Step 7

Cancel the common factor of $s^{5}$ and $s^{8}$ .

Factor $s^{5}$ out of $5 r^{3} s^{5} \cdot 10$ .

$\frac{s^{5} (5 r^{3} \cdot 10)}{s^{8} \cdot 2}$

Cancel the common factors.

Factor $s^{5}$ out of $s^{8} \cdot 2$ .

$\frac{s^{5} (5 r^{3} \cdot 10)}{s^{5} (s^{3} \cdot 2)}$

Cancel the common factor.

$\frac{s^{5} (5 r^{3} \cdot 10)}{s^{5} (s^{3} \cdot 2)}$

Rewrite the expression.

$\frac{5 r^{3} \cdot 10}{s^{3} \cdot 2}$

Step 8

Cancel the common factor of $10$ and $2$ .

Factor $2$ out of $5 r^{3} \cdot 10$ .

$\frac{2 (5 r^{3} \cdot 5)}{s^{3} \cdot 2}$

Cancel the common factors.

Factor $2$ out of $s^{3} \cdot 2$ .

$\frac{2 (5 r^{3} \cdot 5)}{2 \cdot s^{3}}$

Cancel the common factor.

$\frac{2 (5 r^{3} \cdot 5)}{2 \cdot s^{3}}$

Rewrite the expression.

$\frac{5 r^{3} \cdot 5}{s^{3}}$

Step 9

Multiply $5$ by $5$ .

$\frac{25 r^{3}}{s^{3}}$

Simplify ((10rs^3)/(2s^4))÷((2s^4)/(10r^2s^2))

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