Algebra Examples

$\sqrt[3]{\frac{2 t}{3}} = 5$

Step 1

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

${\sqrt[3]{\frac{2 t}{3}}}^{3} = 5^{3}$

Step 2

Simplify each side of the equation.

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{\frac{2 t}{3}}$ as ${(\frac{2 t}{3})}^{\frac{1}{3}}$ .

${({(\frac{2 t}{3})}^{\frac{1}{3}})}^{3} = 5^{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${({(\frac{2 t}{3})}^{\frac{1}{3}})}^{3}$ .

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Step 2.2.1.1

Multiply the exponents in ${({(\frac{2 t}{3})}^{\frac{1}{3}})}^{3}$ .

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Step 2.2.1.1.1

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

${(\frac{2 t}{3})}^{\frac{1}{3} \cdot 3} = 5^{3}$

Step 2.2.1.1.2

Cancel the common factor of $3$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

${(\frac{2 t}{3})}^{\frac{1}{3} \cdot 3} = 5^{3}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(\frac{2 t}{3})}^{1} = 5^{3}$

Step 2.2.1.2

Simplify.

$\frac{2 t}{3} = 5^{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Raise $5$ to the power of $3$ .

$\frac{2 t}{3} = 125$

Step 3

Solve for $t$ .

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Step 3.1

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

$\frac{3}{2} \cdot \frac{2 t}{3} = \frac{3}{2} \cdot 125$

Step 3.2

Simplify both sides of the equation.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Simplify $\frac{3}{2} \cdot \frac{2 t}{3}$ .

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Step 3.2.1.1.1

Cancel the common factor of $3$ .

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Step 3.2.1.1.1.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 t}{3} = \frac{3}{2} \cdot 125$

Step 3.2.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 t) = \frac{3}{2} \cdot 125$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Factor $2$ out of $2 t$ .

$\frac{1}{2} (2 (t)) = \frac{3}{2} \cdot 125$

Step 3.2.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 t) = \frac{3}{2} \cdot 125$

Step 3.2.1.1.2.3

Rewrite the expression.

$t = \frac{3}{2} \cdot 125$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Multiply $\frac{3}{2} \cdot 125$ .

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Step 3.2.2.1.1

Combine $\frac{3}{2}$ and $125$ .

$t = \frac{3 \cdot 125}{2}$

Step 3.2.2.1.2

Multiply $3$ by $125$ .

$t = \frac{375}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$t = \frac{375}{2}$

Decimal Form:

$t = 187.5$

Mixed Number Form:

$t = 187 \frac{1}{2}$