Basic Math Examples

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

Step 1

Apply the product rule to $m^{\frac{1}{4}} n^{\frac{1}{2}}$ .

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

Step 2

Multiply the exponents in ${(m^{\frac{1}{4}})}^{2}$ .

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Step 2.1

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

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

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Factor $2$ out of $4$ .

$m^{\frac{1}{2 (2)} \cdot 2} {(n^{\frac{1}{2}})}^{2} (m^{2} n^{3})$

Step 2.2.2

Cancel the common factor.

$m^{\frac{1}{2 \cdot 2} \cdot 2} {(n^{\frac{1}{2}})}^{2} (m^{2} n^{3})$

Step 2.2.3

Rewrite the expression.

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

Step 3

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

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Step 3.1

Move $m^{2}$ .

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

Step 3.2

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

$m^{2 + \frac{1}{2}} {(n^{\frac{1}{2}})}^{2} n^{3}$

Step 3.3

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

$m^{2 \cdot \frac{2}{2} + \frac{1}{2}} {(n^{\frac{1}{2}})}^{2} n^{3}$

Step 3.4

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

$m^{\frac{2 \cdot 2}{2} + \frac{1}{2}} {(n^{\frac{1}{2}})}^{2} n^{3}$

Step 3.5

Combine the numerators over the common denominator.

$m^{\frac{2 \cdot 2 + 1}{2}} {(n^{\frac{1}{2}})}^{2} n^{3}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $2$ by $2$ .

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

Step 3.6.2

Add $4$ and $1$ .

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Cancel the common factor of $2$ .

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Step 4.2.1

Cancel the common factor.

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

Step 4.2.2

Rewrite the expression.

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

Step 5

Multiply $n^{1}$ by $n^{3}$ by adding the exponents.

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Step 5.1

Move $n^{3}$ .

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

Step 5.2

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

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

Step 5.3

Add $3$ and $1$ .

$m^{\frac{5}{2}} n^{4}$

Step 6

Reorder factors in $m^{\frac{5}{2}} n^{4}$ .

$n^{4} m^{\frac{5}{2}}$