which law would you use to simplify the expression $\frac{3^{10}}{3^{4}}$?\nquotient of powers\npower of a…

Explanation:

Step1: Recall exponent - law definitions

The quotient of powers rule states that $\frac{a^m}{a^n}=a^{m - n}$ for $a\neq0$ and real numbers $m$ and $n$. In the given expression $\frac{3^{10}}{3^{4}}$, $a = 3$, $m = 10$ and $n = 4$.

Step2: Analyze other rules

The power of a quotient is $(\frac{a}{b})^n=\frac{a^n}{b^n}$, the product of powers is $a^m\times a^n=a^{m + n}$, and the power of a power is $(a^m)^n=a^{mn}$, and the power of a product is $(ab)^n=a^n\times b^n$. These do not apply to $\frac{3^{10}}{3^{4}}$.

Answer:

quotient of powers