Algebra II: Fraction Exponent Simplify

Question

How would you get you answer as a fraction exponent?

Answer 1

sqr8 = 2sqr2

cube root of 32 x 2 sqr2 = cube root of 64sqr2

if nothing else you can use a calculator

and round off

sqr2 = 1.414

64 x 1.414 = 90.509668

cube root of 90.509668 = 4.490

that's about 4 1/2 = 9/2

9/2 x 9/2 x 9/2 = 91 1/8= 91.125

it's in the ball park

Answer 2

³√(32√8))

³√(32*2√2))

³√(64 √2))

4 ³√(√2)

4 (2^1/2)^1/3

4 (2^1/6)