Question

I would like somebody to explain how to solve this. i know the answer is 2 3/8, but i don't know how to solve an equation such as this. I'm studying for final exams and need to know how this works, so please help me out.

Answer 1

= 2^(3·1/4·1/2) = 2^(3/8)

Explanation:

You want to simplify ...

`\sqrt{\sqrt[4]{8}}`

Exponent rules

The useful rules of exponents are ...

`\sqrt[n]{a}=a^{(1)/(n)}\\\\(a^b)^c=a^(bc)`

Rewrite

Recognizing 8 = 2³, you can use fractional exponents to represent the roots, then simplify the exponent of the result.

`\sqrt{\sqrt[4]{8}} = ((2^3)^{(1)/(4)})^{(1)/(2)}=2^{3\cdot(1)/(4)\cdot(1)/(2)}=2^{(3)/(4\cdot2)}=\boxed{2^{(3)/(8)}}`

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Additional comment

In plain text, this is written 2^(3/8). Both the caret and the parentheses are required.