Question

Express the following fraction in simplest form using only positive exponents.
start fraction, 5, left parenthesis, v, right parenthesis, cubed, divided by, 3, v, end fraction
3v
5(v)
3

​

Answer 1

To simplify the fraction \(\frac{5v^3}{3v}\), we can follow these steps:

1. **Divide the coefficients**: The coefficient in the numerator is 5 and in the denominator is 3. So, we have:
\[
\frac{5}{3}
\]

2. **Divide the variables**: We have \(v^3\) in the numerator and \(v\) in the denominator. When dividing like bases, we subtract the exponents:
\[
\frac{v^3}{v} = v^{3-1} = v^2
\]

3. **Combine the results**: Now we can combine the coefficient and the variable part:
\[
\frac{5v^3}{3v} = \frac{5}{3} \cdot v^2 = \frac{5v^2}{3}
\]

Thus, the fraction \(\frac{5v^3}{3v}\) in simplest form is:
\[
\frac{5v^2}{3}
\]