2raised to 3 whole power 2+2raised to y is equal to 16 raised to4

find the value of y?

We have,

(2³)^(2+2y) = 16⁴

⇒ 2^3(2+2y) = (2⁴)⁴  [using: (a^m)ⁿ = a^mn]

⇒ 2^{6 + 6y} = 2¹⁶  [Again, using: (a^m)ⁿ = a^mn]

On comparing the power of like terms, we get

6 + 6y = 16

⇒ 6y = 16 - 6 = 10

⇒ y = 10/6 = 5/3