Question

In Exercise,Use properties of exponents to simplyfy the expression. (e2/3)(e3)

Answer 1

Answer: $e^{\frac{11}{3}}$

Step-by-step explanation:

According to the Multiplication property of exponents : $a^m\cdot {a^n}=a^{m+n}$

For example : $2^7\cdot 2^5= 2^{7-5}=2^2$

Let's take one more example , $a^{-11}\cdot a^{1}=a^{-11+1}=a^{-10}$

The given expression : $(e^{\frac{2}{3}})(e^3)$

By Multiplication property of exponents , we have

$(e^{\frac{2}{3}})(e^3)=e^{\frac{2}{3}+3}$

$=e^{\frac{2+3(3)}{3}}=e^{\frac{2+9}{3}}$

$=e^{\frac{11}{3}}$

Hence, the simplified expression is $e^{\frac{11}{3}}$ .