Question
What is the product? \( \frac{5 k}{6} \cdot \frac{3}{2 k^{3}} \)
Ask by Pierce Carrillo. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The product is \( \frac{5}{4k^2} \).
Solution
Calculate or simplify the expression \( \frac{5k}{6} \cdot \frac{3}{2k^3} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{5k}{6}\times \frac{3}{2k^{3}}\)
- step1: Reduce the fraction:
\(\frac{5}{2}\times \frac{1}{2k^{2}}\)
- step2: Multiply the terms:
\(\frac{5}{2\times 2k^{2}}\)
- step3: Multiply the terms:
\(\frac{5}{4k^{2}}\)
The product of \( \frac{5k}{6} \) and \( \frac{3}{2k^3} \) is \( \frac{5}{4k^2} \).
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Simplify this solution Extra Insights
To find the product of the two fractions, we multiply the numerators and the denominators separately: Numerator: \(5k \cdot 3 = 15k\) Denominator: \(6 \cdot 2k^{3} = 12k^{3}\) Now, we combine these to get the overall fraction: \(\frac{15k}{12k^{3}}\) Next, we can simplify this fraction. Both the numerator and denominator can be divided by 3: \(\frac{15k \div 3}{12k^{3} \div 3} = \frac{5k}{4k^{3}}\) We can simplify further by canceling a \(k\) from the numerator and the denominator: \(\frac{5}{4k^{2}}\) So, the final simplified product is: \(\frac{5}{4k^{2}}\)
