Precalculus Examples

${(u - 10)}^{\frac{2}{5}} = 2$

Step 1

Subtract $2$ from both sides of the equation.

${(u - 10)}^{\frac{2}{5}} - 2 = 0$

Step 2

Add $2$ to both sides of the equation.

${(u - 10)}^{\frac{2}{5}} = 2$

Step 3

Raise each side of the equation to the power of $\frac{5}{2}$ to eliminate the fractional exponent on the left side.

${({(u - 10)}^{\frac{2}{5}})}^{\frac{5}{2}} = \pm 2^{\frac{5}{2}}$

Step 4

Simplify the left side.

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Step 4.1

Simplify ${({(u - 10)}^{\frac{2}{5}})}^{\frac{5}{2}}$ .

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Step 4.1.1

Multiply the exponents in ${({(u - 10)}^{\frac{2}{5}})}^{\frac{5}{2}}$ .

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Step 4.1.1.1

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

${(u - 10)}^{\frac{2}{5} \cdot \frac{5}{2}} = \pm 2^{\frac{5}{2}}$

Step 4.1.1.2

Cancel the common factor of $2$ .

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Step 4.1.1.2.1

Cancel the common factor.

${(u - 10)}^{\frac{2}{5} \cdot \frac{5}{2}} = \pm 2^{\frac{5}{2}}$

Step 4.1.1.2.2

Rewrite the expression.

${(u - 10)}^{\frac{1}{5} \cdot 5} = \pm 2^{\frac{5}{2}}$

Step 4.1.1.3

Cancel the common factor of $5$ .

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Step 4.1.1.3.1

Cancel the common factor.

${(u - 10)}^{\frac{1}{5} \cdot 5} = \pm 2^{\frac{5}{2}}$

Step 4.1.1.3.2

Rewrite the expression.

${(u - 10)}^{1} = \pm 2^{\frac{5}{2}}$

Step 4.1.2

Simplify.

$u - 10 = \pm 2^{\frac{5}{2}}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 5.1

First, use the positive value of the $\pm$ to find the first solution.

$u - 10 = 2^{\frac{5}{2}}$

Step 5.2

Add $10$ to both sides of the equation.

$u = 2^{\frac{5}{2}} + 10$

Step 5.3

Next, use the negative value of the $\pm$ to find the second solution.

$u - 10 = - 2^{\frac{5}{2}}$

Step 5.4

Add $10$ to both sides of the equation.

$u = - 2^{\frac{5}{2}} + 10$

Step 5.5

The complete solution is the result of both the positive and negative portions of the solution.

$u = 2^{\frac{5}{2}} + 10, - 2^{\frac{5}{2}} + 10$