Solved on Feb 29, 2024

Evaluate the function y=(14)xy = (\frac{1}{4})^{x} for x=3x = 3.

STEP 1

Assumptions
1. The function is given as y=(14)xy=\left(\frac{1}{4}\right)^{x}.
2. The value of xx is given as x=3x=3.
3. We need to evaluate the function at the given value of xx.

STEP 2

To evaluate the function for the given value of xx, we need to substitute x=3x=3 into the function.
y=(14)xy=\left(\frac{1}{4}\right)^{x}

STEP 3

Substitute x=3x=3 into the function.
y=(14)3y=\left(\frac{1}{4}\right)^{3}

STEP 4

Calculate the value of the function by raising 14\frac{1}{4} to the power of 3.
y=(14)3=14×14×14y=\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 yy.
y=14×14×14=14×4×4y=\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=14×4×4=164y=\frac{1}{4 \times 4 \times 4} = \frac{1}{64}
Therefore, the value of the function when x=3x=3 is y=164y=\frac{1}{64}.
y=164 y=\frac{1}{64}

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