Find the x and y Intercepts y=1/2*(1/4)^x

$y = \frac{1}{2} \cdot {(\frac{1}{4})}^{x}$

Find the x-intercepts.

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

$0 = \frac{1}{2} \cdot {(\frac{1}{4})}^{x}$

Solve the equation.

Rewrite the equation as $\frac{1}{2} \cdot {(\frac{1}{4})}^{x} = 0$ .

$\frac{1}{2} \cdot {(\frac{1}{4})}^{x} = 0$

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot {(\frac{1}{4})}^{x}) = 2 \cdot 0$

Simplify both sides of the equation.

Simplify the left side.

Simplify $2 (\frac{1}{2} \cdot {(\frac{1}{4})}^{x})$ .

Apply the product rule to $\frac{1}{4}$ .

$2 (\frac{1}{2} \cdot \frac{1^{x}}{4^{x}}) = 2 \cdot 0$

Combine.

$2 \frac{1 \cdot 1^{x}}{2 \cdot 4^{x}} = 2 \cdot 0$

Cancel the common factor of $2$ .

Factor $2$ out of $2 \cdot 4^{x}$ .

$2 \frac{1 \cdot 1^{x}}{2 (4^{x})} = 2 \cdot 0$

Cancel the common factor.

$2 \frac{1 \cdot 1^{x}}{2 \cdot 4^{x}} = 2 \cdot 0$

Rewrite the expression.

$\frac{1 \cdot 1^{x}}{4^{x}} = 2 \cdot 0$

Multiply $1$ by $1^{x}$ .

Raise $1$ to the power of $1$ .

$\frac{1^{1} \cdot 1^{x}}{4^{x}} = 2 \cdot 0$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1^{1 + x}}{4^{x}} = 2 \cdot 0$

One to any power is one.

$\frac{1}{4^{x}} = 2 \cdot 0$

Simplify the right side.

Multiply $2$ by $0$ .

$\frac{1}{4^{x}} = 0$

Set the numerator equal to zero.

$1 = 0$

Since $1 \neq 0$ , there are no solutions.

No solution

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

x-intercept(s): $None$

Find the y-intercepts.

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

$y = \frac{1}{2} \cdot {(\frac{1}{4})}^{0}$

Solve the equation.

Remove parentheses.

$y = \frac{1}{2} \cdot {(\frac{1}{4})}^{0}$

Simplify $\frac{1}{2} \cdot {(\frac{1}{4})}^{0}$ .

Apply the product rule to $\frac{1}{4}$ .

$y = \frac{1}{2} \cdot \frac{1^{0}}{4^{0}}$

Combine.

$y = \frac{1 \cdot 1^{0}}{2 \cdot 4^{0}}$

Multiply $1$ by $1^{0}$ by adding the exponents.

Multiply $1$ by $1^{0}$ .

Raise $1$ to the power of $1$ .

$y = \frac{1^{1} \cdot 1^{0}}{2 \cdot 4^{0}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = \frac{1^{1 + 0}}{2 \cdot 4^{0}}$

Add $1$ and $0$ .

$y = \frac{1^{1}}{2 \cdot 4^{0}}$

Simplify $1^{1}$ .

$y = \frac{1}{2 \cdot 4^{0}}$

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

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

Multiply the exponents in ${(2^{2})}^{0}$ .

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

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

Multiply $2$ by $0$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = \frac{1}{2^{1 + 0}}$

Add $1$ and $0$ .

$y = \frac{1}{2^{1}}$

Evaluate the exponent.

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

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{1}{2})$

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, \frac{1}{2})$

Find the x and y Intercepts y=1/2*(1/4)^x

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