Basic Math Examples

$v = 5 a b^{2} + 3 c^{3}$

Step 1

Rewrite the equation as $5 a b^{2} + 3 c^{3} = v$ .

$5 a b^{2} + 3 c^{3} = v$

Step 2

Subtract $5 a b^{2}$ from both sides of the equation.

$3 c^{3} = v - 5 a b^{2}$

Step 3

Divide each term in $3 c^{3} = v - 5 a b^{2}$ by $3$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $3 c^{3} = v - 5 a b^{2}$ by $3$ .

$\frac{3 c^{3}}{3} = \frac{v}{3} + \frac{- 5 a b^{2}}{3}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{3 c^{3}}{3} = \frac{v}{3} + \frac{- 5 a b^{2}}{3}$

Step 3.2.1.2

Divide $c^{3}$ by $1$ .

$c^{3} = \frac{v}{3} + \frac{- 5 a b^{2}}{3}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Move the negative in front of the fraction.

$c^{3} = \frac{v}{3} - \frac{5 a b^{2}}{3}$

Step 4

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

$c = \sqrt[3]{\frac{v}{3} - \frac{5 a b^{2}}{3}}$

Step 5

Simplify $\sqrt[3]{\frac{v}{3} - \frac{5 a b^{2}}{3}}$ .

Tap for more steps...

Step 5.1

Combine the numerators over the common denominator.

$c = \sqrt[3]{\frac{v - 5 a b^{2}}{3}}$

Step 5.2

Reorder $v$ and $- 5 a b^{2}$ .

$c = \sqrt[3]{\frac{- 5 a b^{2} + v}{3}}$

Step 5.3

Rewrite $\sqrt[3]{\frac{- 5 a b^{2} + v}{3}}$ as $\frac{\sqrt[3]{- 5 a b^{2} + v}}{\sqrt[3]{3}}$ .

$c = \frac{\sqrt[3]{- 5 a b^{2} + v}}{\sqrt[3]{3}}$

Step 5.4

Multiply $\frac{\sqrt[3]{- 5 a b^{2} + v}}{\sqrt[3]{3}}$ by $\frac{{\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{2}}$ .

$c = \frac{\sqrt[3]{- 5 a b^{2} + v}}{\sqrt[3]{3}} \cdot \frac{{\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{2}}$

Step 5.5

Combine and simplify the denominator.

Tap for more steps...

Step 5.5.1

Multiply $\frac{\sqrt[3]{- 5 a b^{2} + v}}{\sqrt[3]{3}}$ by $\frac{{\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{2}}$ .

$c = \frac{\sqrt[3]{- 5 a b^{2} + v} {\sqrt[3]{3}}^{2}}{\sqrt[3]{3} {\sqrt[3]{3}}^{2}}$

Step 5.5.2

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

$c = \frac{\sqrt[3]{- 5 a b^{2} + v} {\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{1} {\sqrt[3]{3}}^{2}}$

Step 5.5.3

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

$c = \frac{\sqrt[3]{- 5 a b^{2} + v} {\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{1 + 2}}$

Step 5.5.4

Add $1$ and $2$ .

$c = \frac{\sqrt[3]{- 5 a b^{2} + v} {\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{3}}$

Step 5.5.5

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

Tap for more steps...

Step 5.5.5.1

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

$c = \frac{\sqrt[3]{- 5 a b^{2} + v} {\sqrt[3]{3}}^{2}}{{(3^{\frac{1}{3}})}^{3}}$

Step 5.5.5.2

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

$c = \frac{\sqrt[3]{- 5 a b^{2} + v} {\sqrt[3]{3}}^{2}}{3^{\frac{1}{3} \cdot 3}}$

Step 5.5.5.3

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

$c = \frac{\sqrt[3]{- 5 a b^{2} + v} {\sqrt[3]{3}}^{2}}{3^{\frac{3}{3}}}$

Step 5.5.5.4

Cancel the common factor of $3$ .

Tap for more steps...

Step 5.5.5.4.1

Cancel the common factor.

$c = \frac{\sqrt[3]{- 5 a b^{2} + v} {\sqrt[3]{3}}^{2}}{3^{\frac{3}{3}}}$

Step 5.5.5.4.2

Rewrite the expression.

$c = \frac{\sqrt[3]{- 5 a b^{2} + v} {\sqrt[3]{3}}^{2}}{3^{1}}$

Step 5.5.5.5

Evaluate the exponent.

$c = \frac{\sqrt[3]{- 5 a b^{2} + v} {\sqrt[3]{3}}^{2}}{3}$

Step 5.6

Simplify the numerator.

Tap for more steps...

Step 5.6.1

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

$c = \frac{\sqrt[3]{- 5 a b^{2} + v} \sqrt[3]{3^{2}}}{3}$

Step 5.6.2

Raise $3$ to the power of $2$ .

$c = \frac{\sqrt[3]{- 5 a b^{2} + v} \sqrt[3]{9}}{3}$

Step 5.7

Simplify with factoring out.

Tap for more steps...

Step 5.7.1

Combine using the product rule for radicals.

$c = \frac{\sqrt[3]{(- 5 a b^{2} + v) \cdot 9}}{3}$

Step 5.7.2

Reorder factors in $\frac{\sqrt[3]{(- 5 a b^{2} + v) \cdot 9}}{3}$ .

$c = \frac{\sqrt[3]{9 (- 5 a b^{2} + v)}}{3}$