163/2 + 16 -3/2 = ?

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16^3/2 + 16 ^-3/2 = ?

1. 0
2. 4097/64
3. 1
4. 16/9097

Correct Option: B

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