Algebra Examples

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

Step 1

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

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Step 1.1

Subtract $1$ from both sides of the equation.

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

Step 1.2

Subtract $1$ from $5$ .

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

Step 2

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

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

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

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Step 3.1.1.1

Apply the product rule to $2 x$ .

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

Step 3.1.1.2

Multiply $2$ by $2^{\frac{1}{3}}$ by adding the exponents.

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Step 3.1.1.2.1

Move $2^{\frac{1}{3}}$ .

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

Step 3.1.1.2.2

Multiply $2^{\frac{1}{3}}$ by $2$ .

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Step 3.1.1.2.2.1

Raise $2$ to the power of $1$ .

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

Step 3.1.1.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 3.1.1.2.3

Write $1$ as a fraction with a common denominator.

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

Step 3.1.1.2.4

Combine the numerators over the common denominator.

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

Step 3.1.1.2.5

Add $1$ and $3$ .

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

Step 3.1.1.3

Apply the product rule to $2^{\frac{4}{3}} x^{\frac{1}{3}}$ .

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

Step 3.1.1.4

Multiply the exponents in ${(2^{\frac{4}{3}})}^{3}$ .

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Step 3.1.1.4.1

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

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

Step 3.1.1.4.2

Cancel the common factor of $3$ .

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Step 3.1.1.4.2.1

Cancel the common factor.

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

Step 3.1.1.4.2.2

Rewrite the expression.

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

Step 3.1.1.5

Raise $2$ to the power of $4$ .

$16 {(x^{\frac{1}{3}})}^{3} = 4^{3}$

Step 3.1.1.6

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

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Step 3.1.1.6.1

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

$16 x^{\frac{1}{3} \cdot 3} = 4^{3}$

Step 3.1.1.6.2

Cancel the common factor of $3$ .

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Step 3.1.1.6.2.1

Cancel the common factor.

$16 x^{\frac{1}{3} \cdot 3} = 4^{3}$

Step 3.1.1.6.2.2

Rewrite the expression.

$16 x^{1} = 4^{3}$

Step 3.1.1.7

Simplify.

$16 x = 4^{3}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Raise $4$ to the power of $3$ .

$16 x = 64$

Step 4

Divide each term in $16 x = 64$ by $16$ and simplify.

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Step 4.1

Divide each term in $16 x = 64$ by $16$ .

$\frac{16 x}{16} = \frac{64}{16}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $16$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{16 x}{16} = \frac{64}{16}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{64}{16}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $64$ by $16$ .

$x = 4$