Find the x and y Intercepts f(x)=x^(1/5)

$f (x) = x^{\frac{1}{5}}$

Step 1

Find the x-intercepts.

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

$0 = x^{\frac{1}{5}}$

Solve the equation.

Rewrite the equation as $x^{\frac{1}{5}} = 0$ .

$x^{\frac{1}{5}} = 0$

Raise each side of the equation to the power of $5$ to eliminate the fractional exponent on the left side.

${(x^{\frac{1}{5}})}^{5} = 0^{5}$

Simplify the exponent.

Simplify the left side.

Simplify ${(x^{\frac{1}{5}})}^{5}$ .

Multiply the exponents in ${(x^{\frac{1}{5}})}^{5}$ .

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

$x^{\frac{1}{5} \cdot 5} = 0^{5}$

Cancel the common factor of $5$ .

Cancel the common factor.

$x^{\frac{1}{5} \cdot 5} = 0^{5}$

Rewrite the expression.

$x^{1} = 0^{5}$

Simplify.

$x = 0^{5}$

Simplify the right side.

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

$x = 0$

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 $y$ .

$y = {(0)}^{\frac{1}{5}}$

Solve the equation.

Remove parentheses.

$y = 0^{\frac{1}{5}}$

Remove parentheses.

$y = {(0)}^{\frac{1}{5}}$

Simplify ${(0)}^{\frac{1}{5}}$ .

Simplify the expression.

Rewrite $0$ as $0^{5}$ .

$y = {(0^{5})}^{\frac{1}{5}}$

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

$y = 0^{5 (\frac{1}{5})}$

Cancel the common factor of $5$ .

Cancel the common factor.

$y = 0^{5 (\frac{1}{5})}$

Rewrite the expression.

$y = 0^{1}$

Evaluate the exponent.

$y = 0$

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 f(x)=x^(1/5)

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