Question

Simplify the following and express the result
in the form of negative exponent.
((-2/3)exponent-2)exponent 3
×(1/3)exponent-4×3exponent -1 ×1/12​

Answer 1

Answer:

(2/3)^(-8)

Step-by-step explanation:

((-2/3)exponent-2)exponent 3

×(1/3)exponent-4×3exponent -1 ×1/12​

= [(-2/3)^-2]^3 × [(1/3^-4) ×(3^-1) ×1/12]

= (-2/3)^(-2×3) ×(3^4) × (1/3) ×1/12

= (-2/3)^-6 × (3^4) × (1/3) ×1/12

= (-3/2)^6  × (3^4) × (1/3) ×1/12

= [3^6 × 3^4] / [(2^6) ×(3) × (2^2 × 3)

= 3^(6+4) / [2^(6+2) × 3^2]

= 3^(10-2)/2^8

= 3^8/2^8

= (3/2)^8

= (2/3)^(-8)

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