To calculate: The single radical of the expression \sqrt{x\sqrt{x\sqrt{x}}}

Haven

Haven

Answered question

2021-08-01

To calculate: The single radical of the expression xxx

Answer & Explanation

Cristiano Sears

Cristiano Sears

Skilled2021-08-02Added 96 answers

Step 1
Consider the expression xxx
xxx=(x(x(x12))12)12
Use the product property and the expression becomes,
(x(x(x12))12)12=(x(x1+12)12)12
=(x(x32)12)12
(x x34)12
Add the powers of the same bases.
(x x34)12=(x1+34)12
=(x74)12
=x78
The obtained expression with rational exponents can be rewritten into radicals as.
x78=(x7)18
=x78
Therefore, the value of the expression is =x78

Jeffrey Jordon

Jeffrey Jordon

Expert2021-10-29Added 2605 answers

Answer is given below (on video)

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