Precalculus Examples

${(y - 8)}^{\frac{4}{5}} = 1$

Step 1

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

${({(y - 8)}^{\frac{4}{5}})}^{\frac{5}{4}} = \pm 1^{\frac{5}{4}}$

Step 2

Simplify the exponent.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Simplify ${({(y - 8)}^{\frac{4}{5}})}^{\frac{5}{4}}$ .

Tap for more steps...

Step 2.1.1.1

Multiply the exponents in ${({(y - 8)}^{\frac{4}{5}})}^{\frac{5}{4}}$ .

Tap for more steps...

Step 2.1.1.1.1

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

${(y - 8)}^{\frac{4}{5} \cdot \frac{5}{4}} = \pm 1^{\frac{5}{4}}$

Step 2.1.1.1.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.1.1.1.2.1

Cancel the common factor.

${(y - 8)}^{\frac{4}{5} \cdot \frac{5}{4}} = \pm 1^{\frac{5}{4}}$

Step 2.1.1.1.2.2

Rewrite the expression.

${(y - 8)}^{\frac{1}{5} \cdot 5} = \pm 1^{\frac{5}{4}}$

Step 2.1.1.1.3

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.1.1.1.3.1

Cancel the common factor.

${(y - 8)}^{\frac{1}{5} \cdot 5} = \pm 1^{\frac{5}{4}}$

Step 2.1.1.1.3.2

Rewrite the expression.

${(y - 8)}^{1} = \pm 1^{\frac{5}{4}}$

Step 2.1.1.2

Simplify.

$y - 8 = \pm 1^{\frac{5}{4}}$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

One to any power is one.

$y - 8 = \pm 1$

Step 3

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

Tap for more steps...

Step 3.1

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

$y - 8 = 1$

Step 3.2

Move all terms not containing $y$ to the right side of the equation.

Tap for more steps...

Step 3.2.1

Add $8$ to both sides of the equation.

$y = 1 + 8$

Step 3.2.2

Add $1$ and $8$ .

$y = 9$

Step 3.3

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

$y - 8 = - 1$

Step 3.4

Move all terms not containing $y$ to the right side of the equation.

Tap for more steps...

Step 3.4.1

Add $8$ to both sides of the equation.

$y = - 1 + 8$

Step 3.4.2

Add $- 1$ and $8$ .

$y = 7$

Step 3.5

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

$y = 9, 7$