Basic Math Examples

$2 u^{1 \frac{1}{2}} = m$

Step 1

Simplify the left side.

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Step 1.1

Convert $1 \frac{1}{2}$ to an improper fraction.

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Step 1.1.1

A mixed number is an addition of its whole and fractional parts.

$2 u^{1 + \frac{1}{2}} = m$

Step 1.1.2

Add $1$ and $\frac{1}{2}$ .

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Step 1.1.2.1

Write $1$ as a fraction with a common denominator.

$2 u^{\frac{2}{2} + \frac{1}{2}} = m$

Step 1.1.2.2

Combine the numerators over the common denominator.

$2 u^{\frac{2 + 1}{2}} = m$

Step 1.1.2.3

Add $2$ and $1$ .

$2 u^{\frac{3}{2}} = m$

Step 2

Divide each term in $2 u^{\frac{3}{2}} = m$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 u^{\frac{3}{2}} = m$ by $2$ .

$\frac{2 u^{\frac{3}{2}}}{2} = \frac{m}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor.

$\frac{2 u^{\frac{3}{2}}}{2} = \frac{m}{2}$

Step 2.2.2

Divide $u^{\frac{3}{2}}$ by $1$ .

$u^{\frac{3}{2}} = \frac{m}{2}$

Step 3

Raise each side of the equation to the power of $\frac{2}{3}$ to eliminate the fractional exponent on the left side.

${(u^{\frac{3}{2}})}^{\frac{2}{3}} = {(\frac{m}{2})}^{\frac{2}{3}}$

Step 4

Simplify the exponent.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify ${(u^{\frac{3}{2}})}^{\frac{2}{3}}$ .

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Step 4.1.1.1

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

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Step 4.1.1.1.1

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

$u^{\frac{3}{2} \cdot \frac{2}{3}} = {(\frac{m}{2})}^{\frac{2}{3}}$

Step 4.1.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.1.2.1

Cancel the common factor.

$u^{\frac{3}{2} \cdot \frac{2}{3}} = {(\frac{m}{2})}^{\frac{2}{3}}$

Step 4.1.1.1.2.2

Rewrite the expression.

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

Step 4.1.1.1.3

Cancel the common factor of $2$ .

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Step 4.1.1.1.3.1

Cancel the common factor.

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

Step 4.1.1.1.3.2

Rewrite the expression.

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

Step 4.1.1.2

Simplify.

$u = {(\frac{m}{2})}^{\frac{2}{3}}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Apply the product rule to $\frac{m}{2}$ .

$u = \frac{m^{\frac{2}{3}}}{2^{\frac{2}{3}}}$