How Do You Calculate the 12th Root of x to the Fourth Power?

[EvilScientist]

TL;DR

Finding the root to an exponent that's larger than the root.

I feel incredibly stupid for not getting this. I found this math problem in the beginning of my precalculus book:

12√x^4

That's 12th root of x to the fourth power. How do I find the root of x if the root is larger than the exponent?

 

[Mark44]

Summary: Finding the root to an exponent that's larger than the root.

I feel incredibly stupid for not getting this. I found this math problem in the beginning of my precalculus book:

12√x^4

That's 12th root of x to the fourth power. How do I find the root of x if the root is larger than the exponent?

LaTeX is your friend. See the link to our tutorial in the lower left corner of the input window.

$\sqrt[12]{x^4}$ can be rewritten as $(x^4)^{1/12} = x^{4/12} = x^{1/3}$ using the usual laws of exponents. A simpler form of your expression is $\sqrt[3] x$.

And technically, this is not something to "solve," an action that we can apply to equations or inequalities. What I did was to simplify the expression you wrote.

 

[EvilScientist]

LaTeX is your friend. See the link to our tutorial in the lower left corner of the input window.

$\sqrt[12]{x^4}$ can be rewritten as $(x^4)^{1/12} = x^{4/12} = x^{1/3}$ using the usual laws of exponents. A simpler form of your expression is $\sqrt[3] x$.

And technically, this is not something to "solve," an action that we can apply to equations or inequalities. What I did was to simplify the expression you wrote.

Thank you! It makes a lot more sense to me now. I haven't done this stuff in years and I am trying to brush off my math skills before taking any classes. Needless to say, my math skills are very rusty. Thanks again, I really appreciate it. I'll try learning how to use LaTeX, I'm probably going to need it later.

 

[hutchphd]

I'll try learning how to use LaTeX

Start now! Its like riding a bicycle...maybe less fun to learn.

 

[mcastillo356]

Hi, @EvilScientist , could your question hide a deeper concern? Calculus. I mean, nobody knows the value of $\sqrt[12]{x^{4}}$, if $x=25$, for instance. Only knows can approximate.
LaTeX is fun

 

[DaveE]

Nothing to feel stupid about here. This is really just an issue with not knowing the jargon of that sort of math. We are all stupid about the stuff we haven't learned yet. Go forth and be stupid, ask questions, that's how we all learned this stuff.

 

[Mark44]

Hi, @EvilScientist , could your question hide a deeper concern? Calculus. I mean, nobody knows the value of $\sqrt[12]{x^{4}}$, if $x=25$, for instance. Only knows can approximate.

This has nothing to do with calculus -- $\sqrt[12]{25^{4}} = \sqrt[3]{25}$ is the exact value, but this happens to be irrational, so writing it as a decimal number will be only an approximation. BTW, $\sqrt[3]{25}$ is little less than 3.