Basic Math Examples

$\sqrt[3]{4 + 6 t} - \sqrt[3]{1 - 8 t} = 0$

Step 1

Add $\sqrt[3]{1 - 8 t}$ to both sides of the equation.

$\sqrt[3]{4 + 6 t} = \sqrt[3]{1 - 8 t}$

Step 2

To remove the radical on the left side of the equation, cube both sides of the equation.

${\sqrt[3]{4 + 6 t}}^{3} = {\sqrt[3]{1 - 8 t}}^{3}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{4 + 6 t}$ as ${(4 + 6 t)}^{\frac{1}{3}}$ .

${({(4 + 6 t)}^{\frac{1}{3}})}^{3} = {\sqrt[3]{1 - 8 t}}^{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(4 + 6 t)}^{\frac{1}{3}})}^{3}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(4 + 6 t)}^{\frac{1}{3}})}^{3}$ .

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Step 3.2.1.1.1

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

${(4 + 6 t)}^{\frac{1}{3} \cdot 3} = {\sqrt[3]{1 - 8 t}}^{3}$

Step 3.2.1.1.2

Cancel the common factor of $3$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(4 + 6 t)}^{\frac{1}{3} \cdot 3} = {\sqrt[3]{1 - 8 t}}^{3}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(4 + 6 t)}^{1} = {\sqrt[3]{1 - 8 t}}^{3}$

Step 3.2.1.2

Simplify.

$4 + 6 t = {\sqrt[3]{1 - 8 t}}^{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Rewrite ${\sqrt[3]{1 - 8 t}}^{3}$ as $1 - 8 t$ .

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Step 3.3.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{1 - 8 t}$ as ${(1 - 8 t)}^{\frac{1}{3}}$ .

$4 + 6 t = {({(1 - 8 t)}^{\frac{1}{3}})}^{3}$

Step 3.3.1.2

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

$4 + 6 t = {(1 - 8 t)}^{\frac{1}{3} \cdot 3}$

Step 3.3.1.3

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

$4 + 6 t = {(1 - 8 t)}^{\frac{3}{3}}$

Step 3.3.1.4

Cancel the common factor of $3$ .

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Step 3.3.1.4.1

Cancel the common factor.

$4 + 6 t = {(1 - 8 t)}^{\frac{3}{3}}$

Step 3.3.1.4.2

Rewrite the expression.

$4 + 6 t = {(1 - 8 t)}^{1}$

Step 3.3.1.5

Simplify.

$4 + 6 t = 1 - 8 t$

Step 4

Solve for $t$ .

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Step 4.1

Move all terms containing $t$ to the left side of the equation.

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Step 4.1.1

Add $8 t$ to both sides of the equation.

$4 + 6 t + 8 t = 1$

Step 4.1.2

Add $6 t$ and $8 t$ .

$4 + 14 t = 1$

Step 4.2

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

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Step 4.2.1

Subtract $4$ from both sides of the equation.

$14 t = 1 - 4$

Step 4.2.2

Subtract $4$ from $1$ .

$14 t = - 3$

Step 4.3

Divide each term in $14 t = - 3$ by $14$ and simplify.

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Step 4.3.1

Divide each term in $14 t = - 3$ by $14$ .

$\frac{14 t}{14} = \frac{- 3}{14}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $14$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{14 t}{14} = \frac{- 3}{14}$

Step 4.3.2.1.2

Divide $t$ by $1$ .

$t = \frac{- 3}{14}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Move the negative in front of the fraction.

$t = - \frac{3}{14}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$t = - \frac{3}{14}$

Decimal Form:

$t = - 0.2\overline{142857}$