Question
Simplify. Expres \( \frac{10 p q \cdot 9 p^{5} q^{3}}{10 p q^{5}} \)
Ask by Hobbs Gardner. in the United States
Jan 31,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( \frac{9p^{5}}{q} \).
Solution
Calculate or simplify the expression \( \frac{10pq*9p^5q^3}{10pq^5} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{10pq\times 9p^{5}q^{3}}{10pq^{5}}\)
- step1: Multiply:
\(\frac{90p^{6}q^{4}}{10pq^{5}}\)
- step2: Reduce the fraction:
\(\frac{9p^{5}}{q}\)
The simplified expression is \( \frac{9p^{5}}{q} \).
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Simplify this solution The Deep Dive
To simplify the expression \( \frac{10 p q \cdot 9 p^{5} q^{3}}{10 p q^{5}} \), we first multiply the terms in the numerator: \( 10 p q \cdot 9 p^{5} q^{3} = 90 p^{6} q^{4} \) Now, the expression becomes: \( \frac{90 p^{6} q^{4}}{10 p q^{5}} \) Next, we can simplify by dividing the coefficients and using the laws of exponents: 1. The coefficients: \( \frac{90}{10} = 9 \) 2. For \( p \): \( \frac{p^{6}}{p} = p^{6-1} = p^{5} \) 3. For \( q \): \( \frac{q^{4}}{q^{5}} = q^{4-5} = q^{-1} = \frac{1}{q} \) Putting all of that together, we have: \( 9 p^{5} \cdot \frac{1}{q} = \frac{9 p^{5}}{q} \) So the simplified expression is: \(\frac{9 p^{5}}{q}\)
