170k views
9 votes
Simplify

(Look at the picture)
No links please

Simplify (Look at the picture) No links please-example-1
User Bgibson
by
7.9k points

2 Answers

8 votes

Answer:


\frac{\sqrt[4]{3}}{ \sqrt[5]{3} } = \frac{ {3}^{ (1)/(4) } }{ {3}^{ (1)/(5) } } \\ = {3}^{ (1)/(4) - (1)/(5) } \\ = {3}^{ (5)/(20) - (4)/(20) } \\ = {3}^{ (1)/(20) } \: or \: \sqrt[20]{3}

User Lihongxu
by
8.4k points
11 votes

Answer:


\sqrt[20]{3}

Explanation:

Using the radical rule (
\sqrt[x]{a}=a^{(1)/(x)), we can rewrite the fraction:

(3^1/4)/(3^1/5)

Since we are dividing exponents with the same base, we can subtract the two exponents to get:

3^(1/4-1/5)

Convert both fractions to a base of 20:


(1)/(4)*(5)/(5)=(5)/(20) (notice we can only multiply by a number of itself since it is essentially like multiplying the fraction by 1)


(1)/(5)*(4)/(4)=(4)/(20)

Therefore we have:

3^(5/20-4/20)=3^(1/20)

Which again using the radical rule we can rewrite as:


\sqrt[20]{3}

User Kfuglsang
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories