Maths HELP

Hi, in the question below in the mark scheme it converts 1/2root2 into 2^-3/4, is there a way to work this out?

It converts 1/2root2 into 2^-3/2 using normal indice arithmetic
1/2root2 = 1 / 2^(3/2) = 2^(-3/2)

Yes, so basically the 2√ 2 can be split in to: 2 times √ 2 which in other words is 2¹ times 2^1/2. Now using the power rule, we know that we need to add the indices together so 1 + 1/2 is 3/2. Now we have 1 over 2^3/2 which can be rewritten as 2^-3/2. Hope this helps.