Basic Math Examples

$5 m^{13} cm + 2 m^{4} {cm}^{6} (m \cdot m)$

Step 1

Factor $m^{4} cm$ out of $5 m^{13} cm + 2 m^{4} {cm}^{6} (m \cdot m)$ .

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Step 1.1

Factor $m^{4} cm$ out of $5 m^{13} cm$ .

$m^{4} cm (5 m^{9}) + 2 m^{4} {cm}^{6} (m \cdot m)$

Step 1.2

Factor $m^{4} cm$ out of $2 m^{4} {cm}^{6} (m \cdot m)$ .

$m^{4} cm (5 m^{9}) + m^{4} cm (2 {cm}^{5} (m \cdot m))$

Step 1.3

Factor $m^{4} cm$ out of $m^{4} cm (5 m^{9}) + m^{4} cm (2 {cm}^{5} (m \cdot m))$ .

$m^{4} cm (5 m^{9} + 2 {cm}^{5} (m \cdot m))$

Step 2

Combine exponents.

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Step 2.1

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

$m^{4} cm (5 m^{9} + 2 {cm}^{5} (m^{1} m))$

Step 2.2

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

$m^{4} cm (5 m^{9} + 2 {cm}^{5} (m^{1} m^{1}))$

Step 2.3

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

$m^{4} cm (5 m^{9} + 2 {cm}^{5} m^{1 + 1})$

Step 2.4

Add $1$ and $1$ .

$m^{4} cm (5 m^{9} + 2 {cm}^{5} m^{2})$

Step 3

Factor.

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Step 3.1

Factor $m^{2}$ out of $5 m^{9} + 2 {cm}^{5} m^{2}$ .

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Step 3.1.1

Factor $m^{2}$ out of $5 m^{9}$ .

$m^{4} cm (m^{2} (5 m^{7}) + 2 {cm}^{5} m^{2})$

Step 3.1.2

Factor $m^{2}$ out of $2 {cm}^{5} m^{2}$ .

$m^{4} cm (m^{2} (5 m^{7}) + m^{2} (2 {cm}^{5}))$

Step 3.1.3

Factor $m^{2}$ out of $m^{2} (5 m^{7}) + m^{2} (2 {cm}^{5})$ .

$m^{4} cm (m^{2} (5 m^{7} + 2 {cm}^{5}))$

Step 3.2

Remove unnecessary parentheses.

$m^{4} cm m^{2} (5 m^{7} + 2 {cm}^{5})$

Step 4

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

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Step 4.1

Move $m^{2}$ .

$m^{2} m^{4} cm (5 m^{7} + 2 {cm}^{5})$

Step 4.2

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

$m^{2 + 4} cm (5 m^{7} + 2 {cm}^{5})$

Step 4.3

Add $2$ and $4$ .

$m^{6} cm (5 m^{7} + 2 {cm}^{5})$