163/2 + 16 -3/2 =?

16^3/2 + 16^-3/2
Apply the law of Fractional Exponents and 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