Question
Evaluate the exponential function for the given value of \( x \). \( y=8^{x} \) for \( x=-2 / 3 \) The answer is \( \square \). (Type an integer or a simplified fraction.)
Ask by Little Carroll. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( y = \frac{1}{4} \)
Solution
Substitute \( x=-\frac{2}{3} \) into the expression \( 8^{x} \).
Evaluate the expression by following steps:
- step0: Evaluate:
\(8^{x}\)
- step1: Substitute:
\(8^{-\frac{2}{3}}\)
- step2: Express with a positive exponent:
\(\frac{1}{8^{\frac{2}{3}}}\)
- step3: Simplify:
\(\frac{1}{4}\)
The value of \( y=8^{x} \) when \( x=-\frac{2}{3} \) is \( \frac{1}{4} \) or 0.25.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Extra Insights
To evaluate the exponential function \( y = 8^{x} \) for \( x = -\frac{2}{3} \), we can start by rewriting 8 in terms of base 2. We know that \( 8 = 2^3 \), so: \[ y = (2^3)^{-2/3} \] When raising a power to another power, we multiply the exponents: \[ y = 2^{3 \cdot (-2/3)} = 2^{-2} \] Now, \( 2^{-2} \) can be simplified as: \[ y = \frac{1}{2^{2}} = \frac{1}{4} \] Thus, the answer is \( \frac{1}{4} \).
