Question
Evaluate the exponential function for the given value of \( x \). \( y=8^{x} \) for \( x=-2 \) The answer is \( \square \). (Type an integer or a simplified fraction.)
Ask by Chen Dickson. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The answer is \( \frac{1}{64} \).
Solution
We are given y = 8^x, and we need to find y when x = -2.
Substitute -2 for x:
y = 8^(-2)
Recall that a negative exponent means the reciprocal:
8^(-2) = 1 / (8^2)
Now, calculate 8^2:
8^2 = 64
So:
y = 1 / 64
Therefore, the answer is 1/64.
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Simplify this solution Mind Expander
To evaluate the exponential function \( y=8^{x} \) for \( x=-2 \), we substitute -2 into the equation: \[ y = 8^{-2} \] This can be rewritten using the properties of exponents: \[ y = \frac{1}{8^{2}} = \frac{1}{64} \] So the answer is \( \frac{1}{64} \).
