32sqrt 2 = 2^a, find the value of a

Ok so this is a typical exam questions worth around 3-4 marks depending on which exam board you are sitting with.To start solving this problem, we are looking for 2 to the power of "something" - so we will look to expressing the rest of the equation in terms of "2 to the power of".So we look to 32 which can be expressed as 2⁵.The Sqrt 2 is the same as = 2^1/2.Equation now becomes 2⁵ x 2^1/2 = 2^a.We now recall that when multiplying terms with the same base, the indices can be added. (If this was a division, we would subtract them).Back to our question – our answer then becomes 2^{5 1/2}.Which is better written as 2^11/2.This is identical to 2^a where a=11/2.