Precalculus Examples

$y^{\frac{4}{5}} = 34$

Step 1

Raise each side of the equation to the power of $\frac{5}{4}$ to eliminate the fractional exponent on the left side.

${(y^{\frac{4}{5}})}^{\frac{5}{4}} = \pm 34^{\frac{5}{4}}$

Step 2

Simplify the left side.

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Step 2.1

Simplify ${(y^{\frac{4}{5}})}^{\frac{5}{4}}$ .

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Step 2.1.1

Multiply the exponents in ${(y^{\frac{4}{5}})}^{\frac{5}{4}}$ .

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Step 2.1.1.1

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

$y^{\frac{4}{5} \cdot \frac{5}{4}} = \pm 34^{\frac{5}{4}}$

Step 2.1.1.2

Cancel the common factor of $4$ .

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Step 2.1.1.2.1

Cancel the common factor.

$y^{\frac{4}{5} \cdot \frac{5}{4}} = \pm 34^{\frac{5}{4}}$

Step 2.1.1.2.2

Rewrite the expression.

$y^{\frac{1}{5} \cdot 5} = \pm 34^{\frac{5}{4}}$

Step 2.1.1.3

Cancel the common factor of $5$ .

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Step 2.1.1.3.1

Cancel the common factor.

$y^{\frac{1}{5} \cdot 5} = \pm 34^{\frac{5}{4}}$

Step 2.1.1.3.2

Rewrite the expression.

$y^{1} = \pm 34^{\frac{5}{4}}$

Step 2.1.2

Simplify.

$y = \pm 34^{\frac{5}{4}}$

Step 3

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

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Step 3.1

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

$y = 34^{\frac{5}{4}}$

Step 3.2

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

$y = - 34^{\frac{5}{4}}$

Step 3.3

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

$y = 34^{\frac{5}{4}}, - 34^{\frac{5}{4}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = 34^{\frac{5}{4}}, - 34^{\frac{5}{4}}$

Decimal Form:

$y = 82.10103769 \dots, - 82.10103769 \dots$