what is 49^(-3/2) simplified?

so the first step would be to deal with the minus in the indice, which gives you the reciprocal making it1/49^(3/2)you then approach the rest of the indice which is 3/2, the simplest way to do this is to square root the number getting rid of the 2 on the bottom of the fraction, as the denominator is which root you need to find, and the numerator is how many times you need to times it by itselfso the square root of 49 is 7 so we now have1/7^3to then further simplify the number we need to cube 7 so we do 7 x 7 x 7 which is 343, if you didn't have a calculator we would do 49 x 7 as we already know 7^2 is 49so 40 x 7 which we can break down into (7x4 then x 10 ) which is 280 pus 7 x 9 which is 63 (you could do 7 x 10 then -7)280 + 63 is 343 (which is 0+3 = 3, 8+ 6 = 14 so carry the 1, 2+1 = 3)so the final answer then is1/343