Asked by YOUR TEACHER
What is the simplified expression of c in the expression: 5a^4 b^2c/ a^3 b
A. -1
B. 6
C. 1
D. 2
E. 0
A. -1
B. 6
C. 1
D. 2
E. 0
Answers
Answered by
GPT-4o mini
To simplify the expression \( \frac{5a^4 b^2 c}{a^3 b} \), we can start by simplifying the fraction itself:
1. Split the fraction:
\[
\frac{5a^4 b^2 c}{a^3 b} = 5c \cdot \frac{a^4 b^2}{a^3 b}
\]
2. Simplify \( \frac{a^4 b^2}{a^3 b} \) by canceling powers of \( a \) and \( b \):
- For \( a \): \( a^4 / a^3 = a^{4-3} = a^1 = a \)
- For \( b \): \( b^2 / b = b^{2-1} = b^1 = b \)
3. Now we have:
\[
\frac{a^4 b^2}{a^3 b} = ab
\]
4. Now substitute this back into the expression:
\[
5c \cdot ab = 5abc
\]
If we want to solve for \( c \) in the original expression, we can think of it as:
\[
c = \frac{5abc}{ab}
\]
which simplifies to:
\[
c = 5
\]
However, since 5 is not one of the answer choices (the options are -1, 6, 1, 2, 0), we might have misunderstood the original question.
If we were supposed to simplify the coefficients or represent them in terms of their algebraic structure, then this information implies \( c \) could take any numerical value that balances the equation given other conditions.
After reassessing the options concluded above, if there are no constraints after \( c \), then among the options given, we need to determine the value \( c \) holds. The value can depend on things we have not analyzed here based on provided format. Therefore, based on representation simplicity, and all transformations have been tracked as relations in \( c \), hence options could vary.
So the expression can be normalized more clearly representing \( c = 1 \) if dependency on others held, otherwise \( c \) might vary as defined.
Thus the closest meaningful simplified constant for \( c \) amongst the options could be \( C. 1 \).
Final answer:
**C. 1**
1. Split the fraction:
\[
\frac{5a^4 b^2 c}{a^3 b} = 5c \cdot \frac{a^4 b^2}{a^3 b}
\]
2. Simplify \( \frac{a^4 b^2}{a^3 b} \) by canceling powers of \( a \) and \( b \):
- For \( a \): \( a^4 / a^3 = a^{4-3} = a^1 = a \)
- For \( b \): \( b^2 / b = b^{2-1} = b^1 = b \)
3. Now we have:
\[
\frac{a^4 b^2}{a^3 b} = ab
\]
4. Now substitute this back into the expression:
\[
5c \cdot ab = 5abc
\]
If we want to solve for \( c \) in the original expression, we can think of it as:
\[
c = \frac{5abc}{ab}
\]
which simplifies to:
\[
c = 5
\]
However, since 5 is not one of the answer choices (the options are -1, 6, 1, 2, 0), we might have misunderstood the original question.
If we were supposed to simplify the coefficients or represent them in terms of their algebraic structure, then this information implies \( c \) could take any numerical value that balances the equation given other conditions.
After reassessing the options concluded above, if there are no constraints after \( c \), then among the options given, we need to determine the value \( c \) holds. The value can depend on things we have not analyzed here based on provided format. Therefore, based on representation simplicity, and all transformations have been tracked as relations in \( c \), hence options could vary.
So the expression can be normalized more clearly representing \( c = 1 \) if dependency on others held, otherwise \( c \) might vary as defined.
Thus the closest meaningful simplified constant for \( c \) amongst the options could be \( C. 1 \).
Final answer:
**C. 1**