Problem:
Which of the following is the value of √(³√(0.000064))?

Solution:
One way to go about this calculation – and possibly the simpliest way - is to simplify the exponents before performing any calculations.  Rewrite this problem as:
(((64*10^-6)^1/3)^1/2) (multiply the exponents together – see rule below)
= (64*10^-6)^1/6 (distribute the exponent ^1/6 across the 64 and the 10)
= 64^1/6 * 10^-1  (simplify exponents)
= 2 / 10 = .2

Strategy:
Knowing your exponent rules is critical.  Remember that a square root can be written as the (1/2) exponent.  Similarly, a cubic root can be written as the (1/3) exponent  (and so on…).

Remember these rules (where a and b represent any base, and m and n represent any exponent):

(a^m)ⁿ = a^mn

(ab)ⁿ = aⁿ bⁿ

1   =  a^-n
aⁿ