Express the following fraction in simplest form using only positive exponents.

Question

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: \[ \frac{5v^2}{3} \]