Which of the following is the value of √(3√(0.000064))?
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)
= 641/6 * 10-1 (simplify exponents)
= 2 / 10 = .2
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):
(am)n = amn
(ab)n = an bn
1 = a-n