Question

How do I do a question containing powers that are improper fractions?

say for example 81 to the power of 3/2. thx

Answer 1

`81^{\tfrac{3}{2}}=\\ (3^4)^{\tfrac{3}{2}}=\\ 3^{4\cdot\tfrac{3}{2}}=\\ 3^(2\cdot3)=\\ 3^6=\\ 729`

Answer 2

( 81 )^ ( 3 / 2 ) = ( 3 ^ 4 )^ ( 3 / 2 ) = 3 ^( 4 * 3 / 2 ) = 3 ^ 6 = 729.