Question

simplify. assume all variables are positive.
$v^{\frac{8}{3}} \cdot v^{\frac{1}{3}}$
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: 同底数幂相乘，指数相加

根据同底数幂乘法法则：$a^m \cdot a^n = a^{m+n}$，这里底数为$v$，指数分别为$\frac{8}{3}$和$\frac{1}{3}$，因此：
$v^{\frac{8}{3}} \cdot v^{\frac{1}{3}} = v^{\frac{8}{3}+\frac{1}{3}}$

Step2: 计算指数的和

计算指数部分的加法：
$\frac{8}{3}+\frac{1}{3}=\frac{9}{3}=3$，因此式子化简为$v^3$

Answer:

$v^3$