Find the x and y Intercepts (2x-8)^(2/3)

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

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

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

Find the x-intercepts.

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

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

Solve the equation.

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

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

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

$2 x - 8 = 0$

Solve for $x$ .

Add $8$ to both sides of the equation.

$2 x = 8$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $8$ by $2$ .

$x = 4$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

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

Simplify the expression.

Multiply $2$ by $0$ .

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

Subtract $8$ from $0$ .

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

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

$y = 4$

y-intercept(s) in point form.

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

List the intersections.

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

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

Find the x and y Intercepts (2x-8)^(2/3)

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