Basic Math Examples

$2 (m^{\frac{1}{4}} n^{\frac{1}{2}}) {(k^{3} m^{5})}^{\frac{1}{2}}$

Step 1

Apply the product rule to $k^{3} m^{5}$ .

$2 m^{\frac{1}{4}} n^{\frac{1}{2}} ({(k^{3})}^{\frac{1}{2}} {(m^{5})}^{\frac{1}{2}})$

Step 2

Multiply the exponents in ${(k^{3})}^{\frac{1}{2}}$ .

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Step 2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 m^{\frac{1}{4}} n^{\frac{1}{2}} (k^{3 (\frac{1}{2})} {(m^{5})}^{\frac{1}{2}})$

Step 2.2

Combine $3$ and $\frac{1}{2}$ .

$2 m^{\frac{1}{4}} n^{\frac{1}{2}} (k^{\frac{3}{2}} {(m^{5})}^{\frac{1}{2}})$

Step 3

Multiply the exponents in ${(m^{5})}^{\frac{1}{2}}$ .

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Step 3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 m^{\frac{1}{4}} n^{\frac{1}{2}} (k^{\frac{3}{2}} m^{5 (\frac{1}{2})})$

Step 3.2

Combine $5$ and $\frac{1}{2}$ .

$2 m^{\frac{1}{4}} n^{\frac{1}{2}} (k^{\frac{3}{2}} m^{\frac{5}{2}})$

Step 4

Multiply $m^{\frac{1}{4}}$ by $m^{\frac{5}{2}}$ by adding the exponents.

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Step 4.1

Move $m^{\frac{5}{2}}$ .

$2 (m^{\frac{5}{2}} m^{\frac{1}{4}}) n^{\frac{1}{2}} k^{\frac{3}{2}}$

Step 4.2

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

$2 m^{\frac{5}{2} + \frac{1}{4}} n^{\frac{1}{2}} k^{\frac{3}{2}}$

Step 4.3

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$2 m^{\frac{5}{2} \cdot \frac{2}{2} + \frac{1}{4}} n^{\frac{1}{2}} k^{\frac{3}{2}}$

Step 4.4

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.4.1

Multiply $\frac{5}{2}$ by $\frac{2}{2}$ .

$2 m^{\frac{5 \cdot 2}{2 \cdot 2} + \frac{1}{4}} n^{\frac{1}{2}} k^{\frac{3}{2}}$

Step 4.4.2

Multiply $2$ by $2$ .

$2 m^{\frac{5 \cdot 2}{4} + \frac{1}{4}} n^{\frac{1}{2}} k^{\frac{3}{2}}$

Step 4.5

Combine the numerators over the common denominator.

$2 m^{\frac{5 \cdot 2 + 1}{4}} n^{\frac{1}{2}} k^{\frac{3}{2}}$

Step 4.6

Simplify the numerator.

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Step 4.6.1

Multiply $5$ by $2$ .

$2 m^{\frac{10 + 1}{4}} n^{\frac{1}{2}} k^{\frac{3}{2}}$

Step 4.6.2

Add $10$ and $1$ .

$2 m^{\frac{11}{4}} n^{\frac{1}{2}} k^{\frac{3}{2}}$