Question

simplify. assume all variables are positive.
$v^{\frac{12}{7}}\div v^{\frac{2}{3}}$
write your answer in the form a or $\frac{a}{b}$, where a and b are constants or variable expressions that have no variables in common. all exponents in your answer should be positive.

Explanation:

Step1: Use exponent - division rule

When dividing two powers with the same base \(a^m\div a^n=a^{m - n}\), here \(a = v\), \(m=\frac{12}{7}\), and \(n = \frac{2}{3}\). So \(v^{\frac{12}{7}}\div v^{\frac{2}{3}}=v^{\frac{12}{7}-\frac{2}{3}}\).

Step2: Find a common denominator

The common denominator of 7 and 3 is 21. Then \(\frac{12}{7}-\frac{2}{3}=\frac{12\times3}{7\times3}-\frac{2\times7}{3\times7}=\frac{36}{21}-\frac{14}{21}\).

Step3: Subtract the fractions

\(\frac{36}{21}-\frac{14}{21}=\frac{36 - 14}{21}=\frac{22}{21}\).
So \(v^{\frac{12}{7}}\div v^{\frac{2}{3}}=v^{\frac{22}{21}}\).

Answer:

\(v^{\frac{22}{21}}\)