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anonymous
 one year ago
^3√(2^6)^x
I know that the answer is 4^x but what are the steps to solve?
anonymous
 one year ago
^3√(2^6)^x I know that the answer is 4^x but what are the steps to solve?

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SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0\(\LARGE \displaystyle \left(\sqrt[3]{2^6}\right)^x\) like this?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0parentheses around only the 2^6

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0\(\LARGE \displaystyle\sqrt[3]{ \left(2^6\right)^x}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0well, this is what you can do: \(\LARGE \displaystyle\sqrt[3]{ \left(2^6\right)^x}=\left(\sqrt[3]{ 2^6}\right)^x\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0then, deal with what is inside the parenthesis alone, and if the part inside the parenthesis is a 4, then the expression is 4\(^x\).

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0more percisely. \(\LARGE \displaystyle\sqrt[3]{ \left(2^6\right)^x}=\) \(\LARGE \displaystyle \left(\sqrt[3]{ 2^6}\right)^x=\) \(\LARGE \displaystyle \left(2^{6/3}\right)^x=\) \(\LARGE \displaystyle \left(2^{2}\right)^x=\) \(\LARGE \displaystyle \left(4\right)^x.\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0if you have a question about the validity of the steps (i.e. what propery did I use for a particular step, or why doing something is valid and works, etc) or other questions as wel...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok I understand it now... I just wasn't sure about about what to do with the 6 and the 3 but it makes sense now that I see it. Thank you so much!

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Anytime..... But, what I did in the first step is not alwyas valid, although is in this case.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0For example, if I say: \(\LARGE \sqrt{x^2}=\left( \sqrt{x} \right)^2\) then I am faulty

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Why? because the left side is the absolute value of x (i.e. x ) And it is continous for all values of x over the interval (∞,+∞) And the right side is a line y=x for all values of x, where x≥0 (but undefined for x<0)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0But, you can always use the following property: \(\LARGE \sqrt[a]{x^b}=x^{b/a}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0that is what I used to get from line 2 to line 3
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