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

Haven 2021-08-01 Answered
To calculate: The single radical of the expression xxx
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Expert Answer

Cristiano Sears
Answered 2021-08-02 Author has 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

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Jeffrey Jordon
Answered 2021-10-29 Author has 2027 answers

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