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

Question

(1 point)
Responses

1
1

6
6

-1
-1

2
2

0
0

Answer 1

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

1. Divide the coefficients: The coefficient in the numerator is 5 and in the denominator is 1, so it remains 5.

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

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

4. The \( c \) term: Since there are no \( c \) terms in the denominator, it remains \( c^1 \).

Putting this all together, we have: \[ \frac{5a^4b^2c}{a^3b} = 5a^1b^1c^1 = 5abc \]

In this expression, the exponent of \( c \) is \( 1 \).

Thus, the simplified exponent of \( c \) in the expression is 1.