Algebra Examples

$s = \frac{3}{2} \sqrt[4]{d}$

Step 1

Rewrite the equation as $\frac{3}{2} \cdot \sqrt[4]{d} = s$ .

$\frac{3}{2} \cdot \sqrt[4]{d} = s$

Step 2

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} (\frac{3}{2} \cdot \sqrt[4]{d}) = \frac{2}{3} s$

Step 3

Simplify both sides of the equation.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Simplify $\frac{2}{3} (\frac{3}{2} \cdot \sqrt[4]{d})$ .

Tap for more steps...

Step 3.1.1.1

Combine $\frac{3}{2}$ and $\sqrt[4]{d}$ .

$\frac{2}{3} \cdot \frac{3 \sqrt[4]{d}}{2} = \frac{2}{3} s$

Step 3.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.1.2.1

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 \sqrt[4]{d}}{2} = \frac{2}{3} s$

Step 3.1.1.2.2

Rewrite the expression.

$\frac{1}{3} (3 \sqrt[4]{d}) = \frac{2}{3} s$

Step 3.1.1.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.1.1.3.1

Factor $3$ out of $3 \sqrt[4]{d}$ .

$\frac{1}{3} (3 (\sqrt[4]{d})) = \frac{2}{3} s$

Step 3.1.1.3.2

Cancel the common factor.

$\frac{1}{3} (3 \sqrt[4]{d}) = \frac{2}{3} s$

Step 3.1.1.3.3

Rewrite the expression.

$\sqrt[4]{d} = \frac{2}{3} s$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Combine $\frac{2}{3}$ and $s$ .

$\sqrt[4]{d} = \frac{2 s}{3}$

Step 4

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

${\sqrt[4]{d}}^{4} = {(\frac{2 s}{3})}^{4}$

Step 5

Simplify each side of the equation.

Tap for more steps...

Step 5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{d}$ as $d^{\frac{1}{4}}$ .

${(d^{\frac{1}{4}})}^{4} = {(\frac{2 s}{3})}^{4}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Simplify ${(d^{\frac{1}{4}})}^{4}$ .

Tap for more steps...

Step 5.2.1.1

Multiply the exponents in ${(d^{\frac{1}{4}})}^{4}$ .

Tap for more steps...

Step 5.2.1.1.1

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

$d^{\frac{1}{4} \cdot 4} = {(\frac{2 s}{3})}^{4}$

Step 5.2.1.1.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 5.2.1.1.2.1

Cancel the common factor.

$d^{\frac{1}{4} \cdot 4} = {(\frac{2 s}{3})}^{4}$

Step 5.2.1.1.2.2

Rewrite the expression.

$d^{1} = {(\frac{2 s}{3})}^{4}$

Step 5.2.1.2

Simplify.

$d = {(\frac{2 s}{3})}^{4}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Simplify ${(\frac{2 s}{3})}^{4}$ .

Tap for more steps...

Step 5.3.1.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Tap for more steps...

Step 5.3.1.1.1

Apply the product rule to $\frac{2 s}{3}$ .

$d = \frac{{(2 s)}^{4}}{3^{4}}$

Step 5.3.1.1.2

Apply the product rule to $2 s$ .

$d = \frac{2^{4} s^{4}}{3^{4}}$

Step 5.3.1.2

Raise $2$ to the power of $4$ .

$d = \frac{16 s^{4}}{3^{4}}$

Step 5.3.1.3

Raise $3$ to the power of $4$ .

$d = \frac{16 s^{4}}{81}$