Question

simplify.
\frac{4v^{4}}{24v}

Explanation:

Step1: Simplify the coefficients

Simplify the fraction of the coefficients \( \frac{4}{24} \). We can divide both the numerator and the denominator by their greatest common divisor, which is 4. So, \( \frac{4\div4}{24\div4}=\frac{1}{6} \).

Step2: Simplify the variables using the quotient rule of exponents

For the variables, we use the rule \( \frac{a^m}{a^n}=a^{m - n} \) (where \( a
eq0 \), \( m \) and \( n \) are real numbers). Here, for the variable \( v \), we have \( \frac{v^4}{v^1}=v^{4 - 1}=v^3 \).

Step3: Combine the simplified coefficients and variables

Now, combine the simplified coefficient \( \frac{1}{6} \) and the simplified variable \( v^3 \). So the simplified form of \( \frac{4v^4}{24v} \) is \( \frac{v^3}{6} \).

Answer:

\( \frac{v^3}{6} \)