Question

Rewrite the rational exponent as a radical by extending the properties of integer exponents.

(screenshot below)

Answer 1

@dan815

Answer 2

First apple rule of exponents \(\large \frac{a^m}{a^n}=a^{m-n}\)

Answer 3

*apply

Answer 4

\[2^{\frac{ 7 }{ 8 }}/ 2^{\frac{ 2 }{ 8 }}=2^{\frac{ 5 }{ 8 }}=\sqrt[8]{2^{5}}\]

Answer 5

ohhh thanks can you explain so i understand how to do this on my own :D

Answer 6

Look at what Jadzia said
\[\frac{a^\color{red}m}{a^\color{blue}n}=a^{\color{red}{m}-\color{blue}{n}} \]
Your m is 7/8, your n= 2/8, your a =2 you have
\[\frac{2^\color{red}{7/8}}{2^\color{blue}{2/8}}=2^{(\color{red}{7/8}-\color{blue}{2/8})} \]

Answer 7

and \(\dfrac{7}{8}-\dfrac{2}{8}=\dfrac{5}{8}\) like what unu811 said, you have the answer.
LOLLOLLOL...
you have the method from Jadzia
the result from unu811
and the explanation from me
Hopefully you can do it by yourself. :)

Answer 8

lol :) thanks so much xd one thing how did 8 get on the outside and 5 on the inside?

Answer 9

Because it is the rule of root

Answer 10

Like

Answer 11

it means