Find the x and y Intercepts 8y=x^3

$8 y = x^{3}$

Step 1

Find the x-intercepts.

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

$8 (0) = x^{3}$

Solve the equation.

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

$x^{3} = 8 (0)$

Multiply $8$ by $0$ .

$x^{3} = 0$

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \sqrt[3]{0}$

Simplify $\sqrt[3]{0}$ .

Rewrite $0$ as $0^{3}$ .

$x = \sqrt[3]{0^{3}}$

Pull terms out from under the radical, assuming real numbers.

$x = 0$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$8 y = {(0)}^{3}$

Solve the equation.

Remove parentheses.

$8 y = 0^{3}$

Divide each term in $8 y = 0^{3}$ by $8$ and simplify.

Divide each term in $8 y = 0^{3}$ by $8$ .

$\frac{8 y}{8} = \frac{0^{3}}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 y}{8} = \frac{0^{3}}{8}$

Divide $y$ by $1$ .

$y = \frac{0^{3}}{8}$

Simplify the right side.

Raising $0$ to any positive power yields $0$ .

$y = \frac{0}{8}$

Divide $0$ by $8$ .

$y = 0$

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4

Find the x and y Intercepts 8y=x^3

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