How to simplify fraction exponents? For example (x^3+4x^2+7)^1/4 I know that if the exponent n is an integer, I can use Newton's Binom to simplify. But I have no idea what to do if the exponent is a fraction. My question is, how would you simplify (x^3+4x^2+7)^1/4, or root[4]((x^3+4x^2+7)) ? Are there any formulas for this?

Lustyku8

Lustyku8

Answered question

2022-09-22

How to simplify fraction exponents? For example ( x 3 + 4 x 2 + 7 ) 1 4
I know that if the exponent n is an integer, I can use Newton's Binom to simplify.
But I have no idea what to do if the exponent is a fraction.
My question is, how would you simplify
( x 3 + 4 x 2 + 7 ) 1 4
, or ( x 3 + 4 x 2 + 7 ) 4 ? Are there any formulas for this?

Answer & Explanation

Amiya Watkins

Amiya Watkins

Beginner2022-09-23Added 6 answers

You can rewrite a power of 1 / 4 as a fourth root — that's absolutely correct. However, unless you can factor it (in which case you'll be simplifying a root of a product, which is a whole different story), there is no way to simplify further roots of sums or differences.

Krish Crosby

Krish Crosby

Beginner2022-09-24Added 3 answers

one can write
e ln ( x 3 + 4 x 2 + 7 ) 4

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