Algebra Examples

$\sqrt[5]{x} + 5 = 7$

Step 1

Move all terms not containing $\sqrt[5]{x}$ to the right side of the equation.

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Step 1.1

Subtract $5$ from both sides of the equation.

$\sqrt[5]{x} = 7 - 5$

Step 1.2

Subtract $5$ from $7$ .

$\sqrt[5]{x} = 2$

Step 2

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $5$ .

${\sqrt[5]{x}}^{5} = 2^{5}$

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 $\sqrt[5]{x}$ as $x^{\frac{1}{5}}$ .

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(x^{\frac{1}{5}})}^{5}$ .

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Step 3.2.1.1

Multiply the exponents in ${(x^{\frac{1}{5}})}^{5}$ .

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Step 3.2.1.1.1

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

$x^{\frac{1}{5} \cdot 5} = 2^{5}$

Step 3.2.1.1.2

Cancel the common factor of $5$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

$x^{\frac{1}{5} \cdot 5} = 2^{5}$

Step 3.2.1.1.2.2

Rewrite the expression.

$x^{1} = 2^{5}$

Step 3.2.1.2

Simplify.

$x = 2^{5}$

Step 3.3

Simplify the right side.

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Step 3.3.1

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

$x = 32$