Question

I need help simplifying a radical equation.

Answer 1

\[\frac{ x ^{\frac{ 3 }{ 4 }} }{ x ^{\frac{ 5 }{ 6 }} }\]

Answer 2

@DanJS

Answer 3

do you recall the exponent properties ..like this one

\[\frac{ 1 }{ x^a }=\frac{ x^{-a} }{ 1 }\]

change sides of the fraction, you change the sign on the exponent like that

Answer 4

to re-write it as a multiplication instead

Answer 5

no :/ i don't

Answer 6

\[\huge \frac{ x^\frac{ 3 }{ 4 } }{ x^\frac{ 5 }{ 6 } } = x^{3/4}*x^{-5/6}\]

i think that is a 6 in there, small font to tell, that right?

Answer 7

yeah, see moved the bottom one to the top and changed the sign on the exponent

Answer 8

yes thaat's right

Answer 9

then another property is this, when you multiply like bases to powers

\[\large x^a*x^b = x^{a+b}\]

you add the exponents like that, write those properties down

Answer 10

\[\huge \frac{ x^\frac{ 3 }{ 4 } }{ x^\frac{ 5 }{ 6 } } = x^{3/4}*x^{-5/6}=x^{3/4 + (-5/6)}\]

like that, and you can add those fractions to simplify

Answer 11

okay so what if i turn the fractions into decimals before I add? will that work?

Answer 12

fractions are Exact, some are repeating decimals that you dont write Exactly, i would keep fractions all the time

Answer 13

1/3 = .3333333 repeating forever, not an exact number in decimal form, approx to how many numbers you write down...

Answer 14

okay

Answer 15

Here is a reference thing, you are doing the Exponent Properties, from the first page, those are the key ideas

Answer 16

so adding those fractions, you end up with

x^(-1/12)

use that first rule again, and put it as

1 / x^(1/12)

final answer should have only + exponents probably