Calculus Examples

$\sqrt[4]{2 y - 4} = 1$

Step 1

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $4$ .

${\sqrt[4]{2 y - 4}}^{4} = 1^{4}$

Step 2

Simplify each side of the equation.

Tap for more steps...

Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{2 y - 4}$ as ${(2 y - 4)}^{\frac{1}{4}}$ .

${({(2 y - 4)}^{\frac{1}{4}})}^{4} = 1^{4}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify ${({(2 y - 4)}^{\frac{1}{4}})}^{4}$ .

Tap for more steps...

Step 2.2.1.1

Multiply the exponents in ${({(2 y - 4)}^{\frac{1}{4}})}^{4}$ .

Tap for more steps...

Step 2.2.1.1.1

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

${(2 y - 4)}^{\frac{1}{4} \cdot 4} = 1^{4}$

Step 2.2.1.1.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.2.1.1.2.1

Cancel the common factor.

${(2 y - 4)}^{\frac{1}{4} \cdot 4} = 1^{4}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(2 y - 4)}^{1} = 1^{4}$

Step 2.2.1.2

Simplify.

$2 y - 4 = 1^{4}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

One to any power is one.

$2 y - 4 = 1$

Step 3

Solve for $y$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Add $4$ to both sides of the equation.

$2 y = 1 + 4$

Step 3.1.2

Add $1$ and $4$ .

$2 y = 5$

Step 3.2

Divide each term in $2 y = 5$ by $2$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $2 y = 5$ by $2$ .

$\frac{2 y}{2} = \frac{5}{2}$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{5}{2}$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{5}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{5}{2}$

Decimal Form:

$y = 2.5$

Mixed Number Form:

$y = 2 \frac{1}{2}$