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hello everyone now this is example number two of a problem involving indices now simplify to simplify this problem we need the loss of indices for instance the first part of our question this part here well use this load solve it that x power negative m over n is equals to a 1 over x power positive n over n m over n i mean which is equals to 1 over x nth root then power m this law applies also to the denominator now this other part will apply this law that x raised to m over n is equals to nth root of x power m now solution starting the first part our x is 243 our m is 2 and our n is 5 so we apply this low so our n is 5 so it will be there fifth root of 243 so it will be 1 over 243 then power 2 times cube root of 125 power 2 then over 1 over 9 the square root power three now solving the first part here well have now the fifth root of one of one 1 over 243 is 1 over 3 then squared times the cube root of 125 is uh five so it will be five squared over the square root of one over nine is