What is the simplified exponent of c in the expression: 5a^4b^2c/a^3b

Answer 1

To simplify the expression \( \frac{5a^4b^2c}{a^3b} \), we can break it down step by step.

1. Separate the terms: \[ \frac{5a^4b^2c}{a^3b} = 5 \cdot \frac{a^4}{a^3} \cdot \frac{b^2}{b} \cdot c \]

2. Simplify the \(a\) terms: \[ \frac{a^4}{a^3} = a^{4-3} = a^1 = a \]

3. Simplify the \(b\) terms: \[ \frac{b^2}{b} = b^{2-1} = b^1 = b \]

4. Combine the results: \[ 5 \cdot a \cdot b \cdot c \]

Thus, the expression simplifies to: \[ 5ab c \]

Now, the exponent of \(c\) in the simplified expression \(5abc\) is:

\[ \boxed{1} \]