Algebra Examples

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

Step 1

Write ${(2 x - 8)}^{\frac{2}{3}}$ as an equation.

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

Step 2

Find the x-intercepts.

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Step 2.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = {(2 x - 8)}^{\frac{2}{3}}$

Step 2.2

Solve the equation.

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Step 2.2.1

Rewrite the equation as ${(2 x - 8)}^{\frac{2}{3}} = 0$ .

${(2 x - 8)}^{\frac{2}{3}} = 0$

Step 2.2.2

Set the $2 x - 8$ equal to $0$ .

$2 x - 8 = 0$

Step 2.2.3

Solve for $x$ .

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Step 2.2.3.1

Add $8$ to both sides of the equation.

$2 x = 8$

Step 2.2.3.2

Divide each term in $2 x = 8$ by $2$ and simplify.

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Step 2.2.3.2.1

Divide each term in $2 x = 8$ by $2$ .

$\frac{2 x}{2} = \frac{8}{2}$

Step 2.2.3.2.2

Simplify the left side.

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Step 2.2.3.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.3.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{8}{2}$

Step 2.2.3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{8}{2}$

Step 2.2.3.2.3

Simplify the right side.

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Step 2.2.3.2.3.1

Divide $8$ by $2$ .

$x = 4$

Step 2.3

x-intercept(s) in point form.

x-intercept(s): $(4, 0)$

Step 3

Find the y-intercepts.

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Step 3.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = {(2 (0) - 8)}^{\frac{2}{3}}$

Step 3.2

Solve the equation.

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Step 3.2.1

Remove parentheses.

$y = {(2 (0) - 8)}^{\frac{2}{3}}$

Step 3.2.2

Simplify ${(2 (0) - 8)}^{\frac{2}{3}}$ .

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Step 3.2.2.1

Simplify the expression.

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Step 3.2.2.1.1

Multiply $2$ by $0$ .

$y = {(0 - 8)}^{\frac{2}{3}}$

Step 3.2.2.1.2

Subtract $8$ from $0$ .

$y = {(- 8)}^{\frac{2}{3}}$

Step 3.2.2.1.3

Rewrite $- 8$ as ${(- 2)}^{3}$ .

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

Step 3.2.2.1.4

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

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

Step 3.2.2.2

Cancel the common factor of $3$ .

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Step 3.2.2.2.1

Cancel the common factor.

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

Step 3.2.2.2.2

Rewrite the expression.

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

Step 3.2.2.3

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

$y = 4$

Step 3.3

y-intercept(s) in point form.

y-intercept(s): $(0, 4)$

Step 4

List the intersections.

x-intercept(s): $(4, 0)$

y-intercept(s): $(0, 4)$

Step 5