Question

simplify.
\frac{24v^{7}}{18v^{3}}

Explanation:

Step1: Simplify the coefficients

Simplify the fraction of the coefficients \( \frac{24}{18} \). We can divide both the numerator and the denominator by their greatest common divisor, which is 6. So \( \frac{24\div6}{18\div6}=\frac{4}{3} \).

Step2: Simplify the variable terms

For the variable \( v \), we use the rule of exponents \( \frac{v^m}{v^n}=v^{m - n} \) where \( m = 7 \) and \( n = 3 \). So \( \frac{v^7}{v^3}=v^{7 - 3}=v^4 \).

Step3: Combine the results

Multiply the simplified coefficient and the simplified variable term together. So we have \( \frac{4}{3}\times v^4=\frac{4v^4}{3} \).

Answer:

\( \frac{4v^4}{3} \)