Basic Math Examples

$m^{\frac{1}{2}} (2 + m^{2})$

Step 1

Apply the distributive property.

$m^{\frac{1}{2}} \cdot 2 + m^{\frac{1}{2}} m^{2}$

Step 2

Move $2$ to the left of $m^{\frac{1}{2}}$ .

$2 \cdot m^{\frac{1}{2}} + m^{\frac{1}{2}} m^{2}$

Step 3

Multiply $m^{\frac{1}{2}}$ by $m^{2}$ by adding the exponents.

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Step 3.1

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

$2 \cdot m^{\frac{1}{2}} + m^{\frac{1}{2} + 2}$

Step 3.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$2 \cdot m^{\frac{1}{2}} + m^{\frac{1}{2} + 2 \cdot \frac{2}{2}}$

Step 3.3

Combine $2$ and $\frac{2}{2}$ .

$2 \cdot m^{\frac{1}{2}} + m^{\frac{1}{2} + \frac{2 \cdot 2}{2}}$

Step 3.4

Combine the numerators over the common denominator.

$2 \cdot m^{\frac{1}{2}} + m^{\frac{1 + 2 \cdot 2}{2}}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $2$ by $2$ .

$2 \cdot m^{\frac{1}{2}} + m^{\frac{1 + 4}{2}}$

Step 3.5.2

Add $1$ and $4$ .

$2 \cdot m^{\frac{1}{2}} + m^{\frac{5}{2}}$

$2 m^{\frac{1}{2}} + m^{\frac{5}{2}}$