Question
1) Simplify. Express your answer using positive exponents. \( \frac{8 f^{-2} \cdot 6 f}{2 f^{8}} \)
Ask by Stephens Gross. in the United States
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( \frac{24}{f^{9}} \).
Solution
Calculate or simplify the expression \( 8*f^(-2)*6*f/(2*f^8) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{8f^{-2}\times 6f}{\left(2f^{8}\right)}\)
- step1: Evaluate:
\(\frac{8f^{-2}\times 6f}{2f^{8}}\)
- step2: Multiply:
\(\frac{48f^{-1}}{2f^{8}}\)
- step3: Reduce the fraction:
\(\frac{24}{f^{9}}\)
The simplified expression is \( \frac{24}{f^{9}} \).
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Simplify this solution Beyond the Answer
To simplify the expression \( \frac{8 f^{-2} \cdot 6 f}{2 f^{8}} \), we first simplify the coefficients and then the powers of \( f \). Start with the coefficients: \( \frac{8 \cdot 6}{2} = \frac{48}{2} = 24 \). Now for the \( f \) terms: Combine the exponents in the numerator: \( f^{-2} \cdot f = f^{-2 + 1} = f^{-1} \). So now we have: \[ \frac{24 f^{-1}}{f^8} = 24 \cdot f^{-1 - 8} = 24 f^{-9}. \] To express it using positive exponents, we write: \[ 24 f^{-9} = \frac{24}{f^9}. \] Thus, the simplified form is: \(\frac{24}{f^9}\).
