Question

(81/256​​​)^{-3/4
How to solve☝☝}

Answer 1

= (81/256)^(- 3/4) → you know that: 81 = 3 * 3 * 3 * 3 = 3^4

= [(3^4)/256]^(- 3/4) → you know that: 256 = 4 * 4 * 4 * 4 = 4^4

= [(3^4)/(4^4)]^(- 3/4)

= [(3/4)^4]^(- 3/4) → recall: (x^a)^b = x^(ab)

= (3/4)^[4 * (- 3/4)]

= (3/4)^(- 3) → recall: x^(- a)= 1/x^(a)

= 1/(3/4)^3

= 1/[(3^3) / (4^3)]

= (4^3) / (3^3)

= 64/27