Question

16^3/2 + 16^-3/2 = ?

Answer 1

We know, by laws of exponents,

a^m x aⁿ = a^m+n

a^-m = 1/a^m

⇒16^3/2 + 1/16^3/2

⇒(16^1/2)³ + 1/(16^1/2)³

⇒(4^{2 x 1/2})³ + 1/(4^{2 x 1/2})³

⇒4³ + 1/4³

⇒ 64 + 1/64

⇒ (64 x 64+ 1)/64

= (4096+1)/64

= 4097/64