Algebra Examples

$(12 a^{2} b^{2}) \cdot (\frac{3}{4} a^{3} b^{4})$

Step 1

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

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Step 1.1

Move $a^{3}$ .

$12 (a^{3} a^{2}) b^{2} \cdot (\frac{3}{4} \cdot (b^{4}))$

Step 1.2

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

$12 a^{3 + 2} b^{2} \cdot (\frac{3}{4} \cdot (b^{4}))$

Step 1.3

Add $3$ and $2$ .

$12 a^{5} b^{2} \cdot (\frac{3}{4} \cdot (b^{4}))$

Step 2

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

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Step 2.1

Move $b^{4}$ .

$12 a^{5} (b^{4} b^{2}) \cdot \frac{3}{4}$

Step 2.2

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

$12 a^{5} b^{4 + 2} \cdot \frac{3}{4}$

Step 2.3

Add $4$ and $2$ .

$12 a^{5} b^{6} \cdot \frac{3}{4}$

Step 3

Cancel the common factor of $4$ .

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Step 3.1

Factor $4$ out of $12 a^{5} b^{6}$ .

$4 (3 a^{5} b^{6}) \cdot \frac{3}{4}$

Step 3.2

Cancel the common factor.

$4 (3 a^{5} b^{6}) \cdot \frac{3}{4}$

Step 3.3

Rewrite the expression.

$3 a^{5} b^{6} \cdot 3$

Step 4

Multiply $3$ by $3$ .

$9 a^{5} b^{6}$