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Solved on Feb 29, 2024

Evaluate the function $y = (\frac{1}{4})^{x}$ for $x = 3$ .

STEP 1

Assumptions
1. The function is given as $y=\left(\frac{1}{4}\right)^{x}$ .
2. The value of $x$ is given as $x=3$ .
3. We need to evaluate the function at the given value of $x$ .

STEP 2

To evaluate the function for the given value of $x$ , we need to substitute $x=3$ into the function.
$y=\left(\frac{1}{4}\right)^{x}$

STEP 3

Substitute $x=3$ into the function.
$y=\left(\frac{1}{4}\right)^{3}$

STEP 4

Calculate the value of the function by raising $\frac{1}{4}$ to the power of 3.
$y=\left(\frac{1}{4}\right)^{3} = \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4}$

STEP 5

Multiply the fractions to get the value of $y$ .
$y=\frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} = \frac{1}{4 \times 4 \times 4}$

STEP 6

Calculate the product in the denominator.
$y=\frac{1}{4 \times 4 \times 4} = \frac{1}{64}$
Therefore, the value of the function when $x=3$ is $y=\frac{1}{64}$ .
$y=\frac{1}{64}$

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