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

Answer:

  = 2^(3·1/4·1/2) = 2^(3/8)

Step-by-step explanation:

You want to simplify ...

  $\sqrt{\sqrt[4]{8}}$

Exponent rules

The useful rules of exponents are ...

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

Rewrite

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

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

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Additional comment

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