# How do you solve this? (root to an exponent that's larger than the root)

EvilScientist
TL;DR 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?

Mentor
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{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 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.

• • mfb, DaveC426913, EvilScientist and 1 other person
EvilScientist
LaTeX is your friend. See the link to our tutorial in the lower left corner of the input window.

##\sqrt{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 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.

• berkeman and PeroK
Homework Helper
2022 Award
I'll try learning how to use LaTeX
Start now! Its like riding a bicycle...maybe less fun to learn.

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

• • • 