Basic Math Examples

$(a^{m} b^{m}) \cdot (4 (a^{m + 1} b^{m + 1})) \cdot 2$

Step 1

Remove unnecessary parentheses.

$a^{m} b^{m} \cdot 4 a^{m + 1} b^{m + 1} \cdot 2$

Step 2

Combine exponents.

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Step 2.1

Multiply $a^{m}$ by $a^{m + 1}$ by adding the exponents.

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Step 2.1.1

Move $a^{m + 1}$ .

$a^{m + 1} a^{m} b^{m} \cdot 4 b^{m + 1} \cdot 2$

Step 2.1.2

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

$a^{m + 1 + m} b^{m} \cdot 4 b^{m + 1} \cdot 2$

Step 2.1.3

Add $m$ and $m$ .

$a^{2 m + 1} b^{m} \cdot 4 b^{m + 1} \cdot 2$

Step 2.2

Multiply $b^{m}$ by $b^{m + 1}$ by adding the exponents.

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Step 2.2.1

Move $b^{m + 1}$ .

$a^{2 m + 1} (b^{m + 1} b^{m}) \cdot 4 \cdot 2$

Step 2.2.2

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

$a^{2 m + 1} b^{m + 1 + m} \cdot 4 \cdot 2$

Step 2.2.3

Add $m$ and $m$ .

$a^{2 m + 1} b^{2 m + 1} \cdot 4 \cdot 2$

Step 2.3

Multiply $2$ by $4$ .

$a^{2 m + 1} b^{2 m + 1} \cdot 8$