Question

simplify the following and express Answer in positive index

(e^3/f^2)^-3 x (e^-4/f)^-1

8^1/3 X 4^1/2

Answer 1

(e^3/f^2)^-3 * (e^-4/f)^-1
= (f^2/e^3)^3 * (f/e^-4)
= f^6/e^9 * e^4f
= f^7/e^5

8^(1/3) * 4^(1/2)
since 8=2^3 and 4=2^2, that's just
= 2 * 2
= 4

Answer 2

(e ^ 3 / f ^ 2 ) ^ - 3 = 1 / (e ^ 3 / f ^ 2 ) ^ 3 = 1 / ( e ^ 9 / f ^ 6 ) = f ^ 6 / e ^ 9


( e ^ - 4 / f ) ^ - 1 = 1 / [ ( 1 / e ^ 4 ) / f ] = 1 / [ 1 / ( e ^ 4 * f ) ] = e ^ 4 * f / 1 = e ^ 4 * f


(e ^ 3 / f ^ 2 ) ^ - 3 * ( e ^ - 4 / f ) ^ - 1 = ( f ^ 6 / e ^ 9 ) * e ^ 4 * f = f ^ 6 * f * e ^ 4 / e ^ 9 = f ^ 7 / e ^ 5 = ( f ^ 5 / e ^ 5 ) * f ^ 2 = ( f / e ) ^ 5 * f ^ 2



8 ^ ( 1 / 3 ) = third root ( 8 )

4 ^ ( 1 / 2 ) = sqroot ( 4 )

8 ^ ( 1 / 3 ) * 4 ^ ( 1 / 2 ) = third root ( 8 ) * sqroot ( 4 ) = 2 * 2 = 4