Algebra Examples

$(6 r s^{2}) (s^{3} t^{2}) (\frac{1}{2} r^{4} t^{3})$

Step 1

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

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Step 1.1

Move $r^{4}$ .

$6 (r^{4} r) s^{2} (s^{3} t^{2}) (\frac{1}{2} \cdot (t^{3}))$

Step 1.2

Multiply $r^{4}$ by $r$ .

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Step 1.2.1

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

$6 (r^{4} r^{1}) s^{2} (s^{3} t^{2}) (\frac{1}{2} \cdot (t^{3}))$

Step 1.2.2

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

$6 r^{4 + 1} s^{2} (s^{3} t^{2}) (\frac{1}{2} \cdot (t^{3}))$

Step 1.3

Add $4$ and $1$ .

$6 r^{5} s^{2} (s^{3} t^{2}) (\frac{1}{2} \cdot (t^{3}))$

Step 2

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

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Step 2.1

Move $s^{3}$ .

$6 r^{5} (s^{3} s^{2}) t^{2} (\frac{1}{2} \cdot (t^{3}))$

Step 2.2

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

$6 r^{5} s^{3 + 2} t^{2} (\frac{1}{2} \cdot (t^{3}))$

Step 2.3

Add $3$ and $2$ .

$6 r^{5} s^{5} t^{2} (\frac{1}{2} \cdot (t^{3}))$

Step 3

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

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Step 3.1

Move $t^{3}$ .

$6 r^{5} s^{5} (t^{3} t^{2}) \frac{1}{2}$

Step 3.2

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

$6 r^{5} s^{5} t^{3 + 2} \frac{1}{2}$

Step 3.3

Add $3$ and $2$ .

$6 r^{5} s^{5} t^{5} \frac{1}{2}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Factor $2$ out of $6 r^{5} s^{5} t^{5}$ .

$2 (3 r^{5} s^{5} t^{5}) \frac{1}{2}$

Step 4.2

Cancel the common factor.

$2 (3 r^{5} s^{5} t^{5}) \frac{1}{2}$

Step 4.3

Rewrite the expression.

$3 r^{5} s^{5} t^{5}$