Algebra Examples

$3 {(x^{\frac{1}{4}})}^{\frac{1}{3}} + 2 = 8$

Step 1

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

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Step 1.1

Subtract $2$ from both sides of the equation.

$3 {(x^{\frac{1}{4}})}^{\frac{1}{3}} - 8 = - 2$

Step 1.2

Add $8$ to both sides of the equation.

$3 {(x^{\frac{1}{4}})}^{\frac{1}{3}} = - 2 + 8$

Step 1.3

Add $- 2$ and $8$ .

$3 {(x^{\frac{1}{4}})}^{\frac{1}{3}} = 6$

Step 2

Raise each side of the equation to the power of $3$ to eliminate the fractional exponent on the left side.

${(3 {(x^{\frac{1}{4}})}^{\frac{1}{3}})}^{3} = 6^{3}$

Step 3

Simplify the exponent.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify ${(3 {(x^{\frac{1}{4}})}^{\frac{1}{3}})}^{3}$ .

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Step 3.1.1.1

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

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Step 3.1.1.1.1

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

${(3 x^{\frac{1}{4} \cdot \frac{1}{3}})}^{3} = 6^{3}$

Step 3.1.1.1.2

Multiply $\frac{1}{4} \cdot \frac{1}{3}$ .

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Step 3.1.1.1.2.1

Multiply $\frac{1}{4}$ by $\frac{1}{3}$ .

${(3 x^{\frac{1}{4 \cdot 3}})}^{3} = 6^{3}$

Step 3.1.1.1.2.2

Multiply $4$ by $3$ .

${(3 x^{\frac{1}{12}})}^{3} = 6^{3}$

Step 3.1.1.2

Apply the product rule to $3 x^{\frac{1}{12}}$ .

$3^{3} {(x^{\frac{1}{12}})}^{3} = 6^{3}$

Step 3.1.1.3

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

$27 {(x^{\frac{1}{12}})}^{3} = 6^{3}$

Step 3.1.1.4

Multiply the exponents in ${(x^{\frac{1}{12}})}^{3}$ .

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Step 3.1.1.4.1

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

$27 x^{\frac{1}{12} \cdot 3} = 6^{3}$

Step 3.1.1.4.2

Cancel the common factor of $3$ .

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Step 3.1.1.4.2.1

Factor $3$ out of $12$ .

$27 x^{\frac{1}{3 (4)} \cdot 3} = 6^{3}$

Step 3.1.1.4.2.2

Cancel the common factor.

$27 x^{\frac{1}{3 \cdot 4} \cdot 3} = 6^{3}$

Step 3.1.1.4.2.3

Rewrite the expression.

$27 x^{\frac{1}{4}} = 6^{3}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Raise $6$ to the power of $3$ .

$27 x^{\frac{1}{4}} = 216$

Step 4

Solve for $x$ .

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Step 4.1

Divide each term in $27 x^{\frac{1}{4}} = 216$ by $27$ and simplify.

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Step 4.1.1

Divide each term in $27 x^{\frac{1}{4}} = 216$ by $27$ .

$\frac{27 x^{\frac{1}{4}}}{27} = \frac{216}{27}$

Step 4.1.2

Simplify the left side.

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Step 4.1.2.1

Cancel the common factor.

$\frac{27 x^{\frac{1}{4}}}{27} = \frac{216}{27}$

Step 4.1.2.2

Divide $x^{\frac{1}{4}}$ by $1$ .

$x^{\frac{1}{4}} = \frac{216}{27}$

Step 4.1.3

Simplify the right side.

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Step 4.1.3.1

Divide $216$ by $27$ .

$x^{\frac{1}{4}} = 8$

Step 4.2

Raise each side of the equation to the power of $4$ to eliminate the fractional exponent on the left side.

${(x^{\frac{1}{4}})}^{4} = 8^{4}$

Step 4.3

Simplify the exponent.

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Step 4.3.1

Simplify the left side.

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Step 4.3.1.1

Simplify ${(x^{\frac{1}{4}})}^{4}$ .

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Step 4.3.1.1.1

Multiply the exponents in ${(x^{\frac{1}{4}})}^{4}$ .

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Step 4.3.1.1.1.1

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

$x^{\frac{1}{4} \cdot 4} = 8^{4}$

Step 4.3.1.1.1.2

Cancel the common factor of $4$ .

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Step 4.3.1.1.1.2.1

Cancel the common factor.

$x^{\frac{1}{4} \cdot 4} = 8^{4}$

Step 4.3.1.1.1.2.2

Rewrite the expression.

$x^{1} = 8^{4}$

Step 4.3.1.1.2

Simplify.

$x = 8^{4}$

Step 4.3.2

Simplify the right side.

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Step 4.3.2.1

Raise $8$ to the power of $4$ .

$x = 4096$