Solve for u 2u^1 1/2=m

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

Step 1

Simplify the left side.

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

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.

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

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

Simplify the left side.

Cancel the common factor.

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

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.

Simplify the left side.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

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

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

Solve for u 2u^1 1/2=m

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