Quick Indices problem

Question

I'm not entirely sure whether this is a suitable problem to ask. However, in trying to solve an index problem, I have been getting stuck in the same place for a while.

The question is:

$$(9a^3 b^{-4})^{1/2} \times 2(a^{1/2}b^{−2})^{−2}$$

I know that the answer is
$$6a^{1/2} \times b^{2}$$

But I'm unsure exactly how to get there. I know I must start by expanding; however, I then get stuck.

Answer 1

Try using these two basic principles:

$(a^x)^y = a^{x \cdot y}$

$a^x \cdot a^y = a^{x+y}$

Answer 2

You have $$(9a^3 b^{-4})^{1/2} \times 2(a^{1/2}b^{−2})^{−2} = 9^{1/2}a^{3/2}b^{-2} \times 2a^{-1}b^{4} = \frac{3a^{3/2}}{b^{2}} \times \frac{2b^4}{a} = 6a^{1/2}b^2$$