Algebra Examples

$y = 5 (x^{3} + 4)$

Step 1

Rewrite the equation as $5 (x^{3} + 4) = y$ .

$5 (x^{3} + 4) = y$

Step 2

Divide each term in $5 (x^{3} + 4) = y$ by $5$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $5 (x^{3} + 4) = y$ by $5$ .

$\frac{5 (x^{3} + 4)}{5} = \frac{y}{5}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{5 (x^{3} + 4)}{5} = \frac{y}{5}$

Step 2.2.1.2

Divide $x^{3} + 4$ by $1$ .

$x^{3} + 4 = \frac{y}{5}$

Step 3

Subtract $4$ from both sides of the equation.

$x^{3} = \frac{y}{5} - 4$

Step 4

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \sqrt[3]{\frac{y}{5} - 4}$

Step 5

Simplify $\sqrt[3]{\frac{y}{5} - 4}$ .

Tap for more steps...

Step 5.1

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x = \sqrt[3]{\frac{y}{5} - 4 \cdot \frac{5}{5}}$

Step 5.2

Combine $- 4$ and $\frac{5}{5}$ .

$x = \sqrt[3]{\frac{y}{5} + \frac{- 4 \cdot 5}{5}}$

Step 5.3

Combine the numerators over the common denominator.

$x = \sqrt[3]{\frac{y - 4 \cdot 5}{5}}$

Step 5.4

Multiply $- 4$ by $5$ .

$x = \sqrt[3]{\frac{y - 20}{5}}$

Step 5.5

Rewrite $\sqrt[3]{\frac{y - 20}{5}}$ as $\frac{\sqrt[3]{y - 20}}{\sqrt[3]{5}}$ .

$x = \frac{\sqrt[3]{y - 20}}{\sqrt[3]{5}}$

Step 5.6

Multiply $\frac{\sqrt[3]{y - 20}}{\sqrt[3]{5}}$ by $\frac{{\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{2}}$ .

$x = \frac{\sqrt[3]{y - 20}}{\sqrt[3]{5}} \cdot \frac{{\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{2}}$

Step 5.7

Combine and simplify the denominator.

Tap for more steps...

Step 5.7.1

Multiply $\frac{\sqrt[3]{y - 20}}{\sqrt[3]{5}}$ by $\frac{{\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{2}}$ .

$x = \frac{\sqrt[3]{y - 20} {\sqrt[3]{5}}^{2}}{\sqrt[3]{5} {\sqrt[3]{5}}^{2}}$

Step 5.7.2

Raise $\sqrt[3]{5}$ to the power of $1$ .

$x = \frac{\sqrt[3]{y - 20} {\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{1} {\sqrt[3]{5}}^{2}}$

Step 5.7.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = \frac{\sqrt[3]{y - 20} {\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{1 + 2}}$

Step 5.7.4

Add $1$ and $2$ .

$x = \frac{\sqrt[3]{y - 20} {\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{3}}$

Step 5.7.5

Rewrite ${\sqrt[3]{5}}^{3}$ as $5$ .

Tap for more steps...

Step 5.7.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{5}$ as $5^{\frac{1}{3}}$ .

$x = \frac{\sqrt[3]{y - 20} {\sqrt[3]{5}}^{2}}{{(5^{\frac{1}{3}})}^{3}}$

Step 5.7.5.2

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

$x = \frac{\sqrt[3]{y - 20} {\sqrt[3]{5}}^{2}}{5^{\frac{1}{3} \cdot 3}}$

Step 5.7.5.3

Combine $\frac{1}{3}$ and $3$ .

$x = \frac{\sqrt[3]{y - 20} {\sqrt[3]{5}}^{2}}{5^{\frac{3}{3}}}$

Step 5.7.5.4

Cancel the common factor of $3$ .

Tap for more steps...

Step 5.7.5.4.1

Cancel the common factor.

$x = \frac{\sqrt[3]{y - 20} {\sqrt[3]{5}}^{2}}{5^{\frac{3}{3}}}$

Step 5.7.5.4.2

Rewrite the expression.

$x = \frac{\sqrt[3]{y - 20} {\sqrt[3]{5}}^{2}}{5^{1}}$

Step 5.7.5.5

Evaluate the exponent.

$x = \frac{\sqrt[3]{y - 20} {\sqrt[3]{5}}^{2}}{5}$

Step 5.8

Simplify the numerator.

Tap for more steps...

Step 5.8.1

Rewrite ${\sqrt[3]{5}}^{2}$ as $\sqrt[3]{5^{2}}$ .

$x = \frac{\sqrt[3]{y - 20} \sqrt[3]{5^{2}}}{5}$

Step 5.8.2

Raise $5$ to the power of $2$ .

$x = \frac{\sqrt[3]{y - 20} \sqrt[3]{25}}{5}$

Step 5.9

Simplify with factoring out.

Tap for more steps...

Step 5.9.1

Combine using the product rule for radicals.

$x = \frac{\sqrt[3]{(y - 20) \cdot 25}}{5}$

Step 5.9.2

Reorder factors in $\frac{\sqrt[3]{(y - 20) \cdot 25}}{5}$ .

$x = \frac{\sqrt[3]{25 (y - 20)}}{5}$