Question

Simplify :
(8/27)⁻¹/³ × (25/4)½ × (4/9)⁰ + (125/64)¹/³

Answer 1

The value of (8/27) ^ (-1/3)  ×  (25/4) ^ (1/2) × (4/9)⁰ + (125/64) ^ (1/3)  =  5

(8/27) ^ (-1/3)  ×  (25/4) ^ (1/2) × (4/9)⁰ + (125/64) ^ (1/3)  

= (27/8) ^ (1/3)   ×  {(5/2)²} ^ (1/2)  × 1   +  {(5/4)³} ^ (1/3)  

[ Applying (a/b)⁻¹  =  (b/a)¹ , and a⁰ = 1 ]

= {(3/2)³} ^ (1/3)  ×  (5/2) ^ {2 × (1/2)}  ×  1  +  (5/4) ^ {3 × (1/3)}

[ Applying (aⁿ) ^ (1/n) = a ^ {n × (1/n)} ]

= (3/2) ^ {3 × (1/3)}  ×  (5/2) ^ {(2 × (1/2)} ×  1  +  (5/4)

[ Applying (aⁿ) ^ (1/n) = a ^ {n × (1/n)} ]

= { (3/2)¹ × (5/2)¹ × 1 }  +  (5/4)

= { (3/2) × (5/2) }  +  (5/4)

= { (3 × 5) / (2 × 2) }  +  (5/4)  

=  (15/4) + (5/4)

=  (15 + 5) / 4

= 20/4

= 5