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AngelaB97
 one year ago
what is 6

^3√4
AngelaB97
 one year ago
what is 6  ^3√4

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AngelaB97
 one year ago
Best ResponseYou've already chosen the best response.0what is dw:1441484588912:dw

AngelaB97
 one year ago
Best ResponseYou've already chosen the best response.0how do you rationalize it?

triciaal
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441486622928:dw

triciaal
 one year ago
Best ResponseYou've already chosen the best response.1to rationalize the denominator means to get rid of the radical. multiply by 1 expressed as a fraction

AngelaB97
 one year ago
Best ResponseYou've already chosen the best response.0before you continue can i just ask is there some sort of rule for what you did when you crossed out those fractions. Meaning, could i be able to do that with any sort of radical that i want to rationalize?

triciaal
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441486781234:dw

triciaal
 one year ago
Best ResponseYou've already chosen the best response.1rules for exponents the nth root is the same as a fractional exponent.

AngelaB97
 one year ago
Best ResponseYou've already chosen the best response.0the answer is supposed to be dw:1441486876177:dw

Excalibur0126
 one year ago
Best ResponseYou've already chosen the best response.0Or in decimal form, 3.7797631...

triciaal
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441486898347:dw

triciaal
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441487116337:dwdw:1441487355866:dw

triciaal
 one year ago
Best ResponseYou've already chosen the best response.1I think I messed up on something @zepdrix please correct

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Hey Angela :) In order to rationalize this thing, you'd like the power on the 4 to be a 1. I like the first step that Tricia applied, writing the 4 with a rational exponent.\[\large\rm \frac{6}{\sqrt[3]{4}}=\frac{6}{4^{1/3}}\]So we don't want a 1/3 power, we want a 1 power down there. What do we have to add to 1/3 to get 1?

AngelaB97
 one year ago
Best ResponseYou've already chosen the best response.0hey :)) we have to add 2/3

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Good good good. We would like 2/3 exponent, we'll leave the base the same. So we actually want to multiply top and bottom by \(\large\rm 4^{2/3}\) Our rules of exponents will give us \(\large\rm 4^{1/3}\cdot4^{2/3}=4^{1/3+2/3}\) in the denominator!

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm \frac{6}{4^{1/3}}\left(\frac{4^{2/3}}{4^{2/3}}\right)=\frac{6\cdot4^{2/3}}{4^{3/3}}\]Ok with that step Angela? :o

triciaal
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441488139781:dw

AngelaB97
 one year ago
Best ResponseYou've already chosen the best response.06 * 42/3 divided by 4

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm \frac{\color{orangered}{6}\cdot 4^{2/3}}{\color{orangered}{4}}\]Mmmm k good. This can be simplified a little bit further since 6 and 4 share a common factor.

AngelaB97
 one year ago
Best ResponseYou've already chosen the best response.0so on the bottom we get 2 and the 6 turns into a 3?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm \frac{3\cdot4^{2/3}}{2}\]Yayyyy good job \c:/

AngelaB97
 one year ago
Best ResponseYou've already chosen the best response.0so we don't need to do any further simplifying? because the answer in my book shows dw:1441488618998:dw @zepdrix

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1OH interesting :O Ok sec I think about it

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Ok maybe this is a better route to take then..\[\large\rm \frac{6}{4^{1/3}}=\frac{3\cdot2}{4^{1/3}}=\frac{3\cdot2}{(2^2)^{1/3}}=\frac{3\cdot2}{2^{2/3}}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1I'm rewriting the 6 as 3*2. I'm rewriting 4 as 2 squared. and then applying exponent rule, when we have a power and a power like that, we multiply. So 2 times 1/3 gave me 2/3 for the power on the 2.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm =\frac{3\cdot2^1}{2^{2/3}}\]And now we can apply one of our exponent rules from here: \(\large\rm \frac{x^{a}}{x^b}=x^{ab}\) Do you see how we can apply that to the 2's?

AngelaB97
 one year ago
Best ResponseYou've already chosen the best response.0yes thank you very much

triciaal
 one year ago
Best ResponseYou've already chosen the best response.1@AngelaB97 sorry if we confuse you but hopefully you understand more about the rules of exponents and how to rationalize it is very easy to make mistakes if not careful

AngelaB97
 one year ago
Best ResponseYou've already chosen the best response.0@zepdrix @triciaal thank you both for your help!
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