Find the x and y Intercepts y=1/8x^(3/2)-8

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

Find the x-intercepts.

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

$0 = \frac{1}{8} x^{\frac{3}{2}} - 8$

Solve the equation.

Rewrite the equation as $\frac{1}{8} x^{\frac{3}{2}} - 8 = 0$ .

$\frac{1}{8} x^{\frac{3}{2}} - 8 = 0$

Add $8$ to both sides of the equation.

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

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

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

Simplify the exponent.

Simplify the left side.

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

Combine fractions.

Combine $\frac{1}{8}$ and $x^{\frac{3}{2}}$ .

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

Apply the product rule to $\frac{x^{\frac{3}{2}}}{8}$ .

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

Simplify the numerator.

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the denominator.

Rewrite $8$ as $2^{3}$ .

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

$\frac{x}{4} = 8^{\frac{2}{3}}$

Simplify the right side.

Simplify $8^{\frac{2}{3}}$ .

Simplify the expression.

Rewrite $8$ as $2^{3}$ .

$\frac{x}{4} = {(2^{3})}^{\frac{2}{3}}$

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

$\frac{x}{4} = 2^{3 (\frac{2}{3})}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{x}{4} = 2^{3 (\frac{2}{3})}$

Rewrite the expression.

$\frac{x}{4} = 2^{2}$

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

$\frac{x}{4} = 4$

Solve for $x$ .

Multiply both sides of the equation by $4$ .

$4 \frac{x}{4} = 4 \cdot 4$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{x}{4} = 4 \cdot 4$

Rewrite the expression.

$x = 4 \cdot 4$

Simplify the right side.

Multiply $4$ by $4$ .

$x = 16$

x-intercept(s) in point form.

x-intercept(s): $(16, 0)$

Find the y-intercepts.

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

$y = \frac{1}{8} \cdot {(0)}^{\frac{3}{2}} - 8$

Solve the equation.

Remove parentheses.

$y = \frac{1}{8} \cdot 0^{\frac{3}{2}} - 8$

Remove parentheses.

$y = \frac{1}{8} \cdot {(0)}^{\frac{3}{2}} - 8$

Simplify $\frac{1}{8} \cdot {(0)}^{\frac{3}{2}} - 8$ .

Simplify each term.

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

$y = \frac{1}{8} \cdot {(0^{2})}^{\frac{3}{2}} - 8$

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

$y = \frac{1}{8} \cdot 0^{2 (\frac{3}{2})} - 8$

Cancel the common factor of $2$ .

Cancel the common factor.

$y = \frac{1}{8} \cdot 0^{2 (\frac{3}{2})} - 8$

Rewrite the expression.

$y = \frac{1}{8} \cdot 0^{3} - 8$

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

$y = \frac{1}{8} \cdot 0 - 8$

Multiply $\frac{1}{8}$ by $0$ .

$y = 0 - 8$

Subtract $8$ from $0$ .

$y = - 8$

y-intercept(s) in point form.

y-intercept(s): $(0, - 8)$

List the intersections.

x-intercept(s): $(16, 0)$

y-intercept(s): $(0, - 8)$

Find the x and y Intercepts y=1/8x^(3/2)-8

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