Question

lesson 4: properties of exponents: division
ns: simplify. write answer in standard form.
= 64

1. $\frac{7^{5}cdot7^{3}}{7^{2}}$

Explanation:

Step1: Use exponent - product rule

According to the rule $a^m\cdot a^n=a^{m + n}$, for $7^5\cdot7^3$, we have $7^5\cdot7^3=7^{5 + 3}=7^8$.
So the expression becomes $\frac{7^8}{7^2}$.

Step2: Use exponent - quotient rule

According to the rule $\frac{a^m}{a^n}=a^{m - n}$ ($a
eq0$), for $\frac{7^8}{7^2}$, we have $7^{8-2}$.
$7^{8 - 2}=7^6$.

Step3: Calculate the value

$7^6=117649$.

Answer:

$117649$