Algebra Examples

$x^{\frac{2}{3}} = 2 x^{\frac{1}{3}}$

Step 1

Eliminate the fractional exponents by multiplying both exponents by the LCD.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Cancel the common factor of $3$ .

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Step 2.2.1

Cancel the common factor.

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

Step 2.2.2

Rewrite the expression.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Raise $2$ to the power of $3$ .

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

Step 3.3

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

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Step 3.3.1

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

$x^{2} = 8 x^{\frac{1}{3} \cdot 3}$

Step 3.3.2

Cancel the common factor of $3$ .

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Step 3.3.2.1

Cancel the common factor.

$x^{2} = 8 x^{\frac{1}{3} \cdot 3}$

Step 3.3.2.2

Rewrite the expression.

$x^{2} = 8 x^{1}$

Step 3.4

Simplify.

$x^{2} = 8 x$

Step 4

Subtract $8 x$ from both sides of the equation.

$x^{2} - 8 x = 0$

Step 5

Factor $x$ out of $x^{2} - 8 x$ .

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Step 5.1

Factor $x$ out of $x^{2}$ .

$x \cdot x - 8 x = 0$

Step 5.2

Factor $x$ out of $- 8 x$ .

$x \cdot x + x \cdot - 8 = 0$

Step 5.3

Factor $x$ out of $x \cdot x + x \cdot - 8$ .

$x (x - 8) = 0$

Step 6

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x - 8 = 0$

Step 7

Set $x$ equal to $0$ .

$x = 0$

Step 8

Set $x - 8$ equal to $0$ and solve for $x$ .

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Step 8.1

Set $x - 8$ equal to $0$ .

$x - 8 = 0$

Step 8.2

Add $8$ to both sides of the equation.

$x = 8$

Step 9

The final solution is all the values that make $x (x - 8) = 0$ true.

$x = 0, 8$