July 20, 2010
**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} = a^{n} b^{n}

1 = a^{-n}

a^{n}

## Connect with Us