Basic Math Examples

$\sqrt[3]{3 y - 2 y} = 3$

Step 1

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

${\sqrt[3]{3 y - 2 y}}^{3} = 3^{3}$

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 $\sqrt[3]{3 y - 2 y}$ as ${(3 y - 2 y)}^{\frac{1}{3}}$ .

${({(3 y - 2 y)}^{\frac{1}{3}})}^{3} = 3^{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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Step 2.2.1.1

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

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Step 2.2.1.1.1

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

${(3 y - 2 y)}^{\frac{1}{3} \cdot 3} = 3^{3}$

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.

${(3 y - 2 y)}^{\frac{1}{3} \cdot 3} = 3^{3}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(3 y - 2 y)}^{1} = 3^{3}$

Step 2.2.1.2

Subtract $2 y$ from $3 y$ .

$y^{1} = 3^{3}$

Step 2.2.1.3

Simplify.

$y = 3^{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

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

$y = 27$