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

Question

options:

1
1

0
0

-1
-1

2
2

6

Answer 1

To simplify the expression \(\frac{5a^{b^2}c}{a^3b}\), we can first focus on the \(a\) terms in the numerator and denominator.

The expression can be rewritten by separating the terms:

\[ \frac{5a^{b^2}c}{a^3b} = 5c \cdot \frac{a^{b^2}}{a^3} \cdot \frac{1}{b} \]

Now we use the property of exponents which says that \(\frac{a^m}{a^n} = a^{m-n}\):

\[ \frac{a^{b^2}}{a^3} = a^{b^2 - 3} \]

Thus, the expression simplifies to:

\[ 5c \cdot a^{b^2 - 3} \cdot \frac{1}{b} \]

Now, looking at the simplified expression, we can identify the term \(c\) which is raised to the exponent of 1 (since \(c^1 = c\)).

Therefore, the simplified exponent of \(c\) in the expression \(\frac{5a^{b^2}c}{a^3b}\) is:

1

So the answer is 1.