Question
Simplify: \( \frac{20 r^{5} s^{2}}{26 r^{5} s^{6}} \)
Ask by Bright Dawson. in the United States
Mar 01,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( \frac{10}{13s^{4}} \).
Solution
To simplify the expression (20r⁵s²) / (26r⁵s⁶), follow these steps:
1. Cancel r⁵ from the numerator and denominator.
2. Simplify the numerical coefficients: 20/26 simplifies to 10/13.
3. Simplify the s terms: s²/s⁶ = s^(2−6) = s⁻⁴ = 1/s⁴.
The final simplified expression is:
10 / (13s⁴)
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Simplify this solution Extra Insights
To simplify the expression \( \frac{20 r^{5} s^{2}}{26 r^{5} s^{6}} \), we start by simplifying the coefficients and the variables separately. First, we simplify the coefficients: \[ \frac{20}{26} = \frac{10}{13} \] Next, we simplify the \( r^{5} \) variables in the numerator and denominator, which cancel each other out, resulting in \( 1 \). Now, we simplify the \( s \) variables: \[ \frac{s^{2}}{s^{6}} = s^{2-6} = s^{-4} \] Putting it all together, we have: \[ \frac{10}{13} \cdot 1 \cdot s^{-4} = \frac{10}{13 s^{4}} \] Thus, the simplified expression is: \[ \frac{10}{13 s^{4}} \]
