root isn't a real number

Question

please help !!!!

Evaluate the root without using a calculator, or note that the root isn't a real number

1) ^4√16

2) ^8√256

Answer 1

I'll take a different shot at it.

4√16 = 4*4=16

or this way:

4√16 = (2²)(2⁴)^1/2 = (2²)(2²) = 2⁴ = 16

8√256 = 8*16=128

or

8√256 = (2³)(2⁸)^1/2 = (2³)(2⁴) = 2⁷= 128

Your use of the carets is confusing.

does ^4√16 mean (√16)⁴?

If so,

(√16)⁴ = [(2⁴)^1/2]⁴ = (2²)⁴ = 2⁸ = 256

but I think not.

Answer 2

The best I can do is

162^1/4_*256^1/8=(2*81)^1/4*2=2^1/4*3*2=6*2^1/4