Algebra Examples

$\frac{(8 r^{5} s^{2}) (3 r^{3} s^{4})}{12 r s^{4}} + 9 r^{7} s^{2}$

Step 1

Simplify each term.

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Step 1.1

Multiply $r^{5}$ by $r^{3}$ by adding the exponents.

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Step 1.1.1

Move $r^{3}$ .

$\frac{8 (r^{3} r^{5}) s^{2} (3 s^{4})}{12 r s^{4}} + 9 r^{7} s^{2}$

Step 1.1.2

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

$\frac{8 r^{3 + 5} s^{2} (3 s^{4})}{12 r s^{4}} + 9 r^{7} s^{2}$

Step 1.1.3

Add $3$ and $5$ .

$\frac{8 r^{8} s^{2} (3 s^{4})}{12 r s^{4}} + 9 r^{7} s^{2}$

Step 1.2

Multiply $s^{2}$ by $s^{4}$ by adding the exponents.

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Step 1.2.1

Move $s^{4}$ .

$\frac{8 r^{8} (s^{4} s^{2}) \cdot 3}{12 r s^{4}} + 9 r^{7} s^{2}$

Step 1.2.2

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

$\frac{8 r^{8} s^{4 + 2} \cdot 3}{12 r s^{4}} + 9 r^{7} s^{2}$

Step 1.2.3

Add $4$ and $2$ .

$\frac{8 r^{8} s^{6} \cdot 3}{12 r s^{4}} + 9 r^{7} s^{2}$

Step 1.3

Cancel the common factor of $8$ and $12$ .

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Step 1.3.1

Factor $4$ out of $8 r^{8} s^{6} \cdot 3$ .

$\frac{4 (2 r^{8} s^{6} \cdot 3)}{12 r s^{4}} + 9 r^{7} s^{2}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $4$ out of $12 r s^{4}$ .

$\frac{4 (2 r^{8} s^{6} \cdot 3)}{4 (3 r s^{4})} + 9 r^{7} s^{2}$

Step 1.3.2.2

Cancel the common factor.

$\frac{4 (2 r^{8} s^{6} \cdot 3)}{4 (3 r s^{4})} + 9 r^{7} s^{2}$

Step 1.3.2.3

Rewrite the expression.

$\frac{2 r^{8} s^{6} \cdot 3}{3 r s^{4}} + 9 r^{7} s^{2}$

Step 1.4

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

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Step 1.4.1

Factor $r$ out of $2 r^{8} s^{6} \cdot 3$ .

$\frac{r (2 r^{7} s^{6} \cdot 3)}{3 r s^{4}} + 9 r^{7} s^{2}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $r$ out of $3 r s^{4}$ .

$\frac{r (2 r^{7} s^{6} \cdot 3)}{r (3 s^{4})} + 9 r^{7} s^{2}$

Step 1.4.2.2

Cancel the common factor.

$\frac{r (2 r^{7} s^{6} \cdot 3)}{r (3 s^{4})} + 9 r^{7} s^{2}$

Step 1.4.2.3

Rewrite the expression.

$\frac{2 r^{7} s^{6} \cdot 3}{3 s^{4}} + 9 r^{7} s^{2}$

Step 1.5

Cancel the common factor of $s^{6}$ and $s^{4}$ .

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Step 1.5.1

Factor $s^{4}$ out of $2 r^{7} s^{6} \cdot 3$ .

$\frac{s^{4} (2 r^{7} s^{2} \cdot 3)}{3 s^{4}} + 9 r^{7} s^{2}$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor $s^{4}$ out of $3 s^{4}$ .

$\frac{s^{4} (2 r^{7} s^{2} \cdot 3)}{s^{4} \cdot 3} + 9 r^{7} s^{2}$

Step 1.5.2.2

Cancel the common factor.

$\frac{s^{4} (2 r^{7} s^{2} \cdot 3)}{s^{4} \cdot 3} + 9 r^{7} s^{2}$

Step 1.5.2.3

Rewrite the expression.

$\frac{2 r^{7} s^{2} \cdot 3}{3} + 9 r^{7} s^{2}$

Step 1.6

Cancel the common factor of $3$ .

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Step 1.6.1

Cancel the common factor.

$\frac{2 r^{7} s^{2} \cdot 3}{3} + 9 r^{7} s^{2}$

Step 1.6.2

Divide $2 r^{7} s^{2}$ by $1$ .

$2 r^{7} s^{2} + 9 r^{7} s^{2}$

Step 2

Add $2 r^{7} s^{2}$ and $9 r^{7} s^{2}$ .

$11 r^{7} s^{2}$