Find the x and y Intercepts f(x)=1/2x^(3/2)

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

Find the x-intercepts.

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

$0 = \frac{1}{2} x^{\frac{3}{2}}$

Solve the equation.

Rewrite the equation as $\frac{1}{2} x^{\frac{3}{2}} = 0$ .

$\frac{1}{2} x^{\frac{3}{2}} = 0$

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} x^{\frac{3}{2}}) = 2 \cdot 0$

Simplify both sides of the equation.

Simplify the left side.

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

Combine $\frac{1}{2}$ and $x^{\frac{3}{2}}$ .

$2 \frac{x^{\frac{3}{2}}}{2} = 2 \cdot 0$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{x^{\frac{3}{2}}}{2} = 2 \cdot 0$

Rewrite the expression.

$x^{\frac{3}{2}} = 2 \cdot 0$

Simplify the right side.

Multiply $2$ by $0$ .

$x^{\frac{3}{2}} = 0$

Raise each side of the equation to the power of $\frac{2}{3}$ to eliminate the fractional exponent on the left side.

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

Simplify the exponent.

Simplify the left side.

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

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

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

$x^{\frac{3}{2} \cdot \frac{2}{3}} = 0^{\frac{2}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x^{\frac{3}{2} \cdot \frac{2}{3}} = 0^{\frac{2}{3}}$

Rewrite the expression.

$x^{\frac{1}{2} \cdot 2} = 0^{\frac{2}{3}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 0^{\frac{2}{3}}$

Rewrite the expression.

$x^{1} = 0^{\frac{2}{3}}$

Simplify.

$x = 0^{\frac{2}{3}}$

Simplify the right side.

Simplify $0^{\frac{2}{3}}$ .

Simplify the expression.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$x = 0^{2}$

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

$x = 0$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

$y = \frac{1}{2} \cdot {(0)}^{\frac{3}{2}}$

Solve the equation.

Remove parentheses.

$y = \frac{1}{2} \cdot 0^{\frac{3}{2}}$

Remove parentheses.

$y = \frac{1}{2} \cdot {(0)}^{\frac{3}{2}}$

Simplify $\frac{1}{2} \cdot {(0)}^{\frac{3}{2}}$ .

Simplify the expression.

Rewrite $0$ as $0^{2}$ .

$y = \frac{1}{2} \cdot {(0^{2})}^{\frac{3}{2}}$

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

$y = \frac{1}{2} \cdot 0^{2 (\frac{3}{2})}$

Cancel the common factor of $2$ .

Cancel the common factor.

$y = \frac{1}{2} \cdot 0^{2 (\frac{3}{2})}$

Rewrite the expression.

$y = \frac{1}{2} \cdot 0^{3}$

Simplify the expression.

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

$y = \frac{1}{2} \cdot 0$

Multiply $\frac{1}{2}$ by $0$ .

$y = 0$

y-intercept(s) in point form.

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

List the intersections.

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

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

Find the x and y Intercepts f(x)=1/2x^(3/2)

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