Write 16 × 8^(2x) as a power of 2 in terms of x

Aim: Our answer should be written in the form 2a+bx where a and b are constants that we are trying to find.
Firstly, we can write 16 in terms of a power of 2: 16 = 42 = 4 x 4 = (2 x 2) x (2 x 2) = 24
Similarly, 8 can be written as a power of 2: 8 = 2 x 4 = 2 x 2 x 2 = 23
Putting this together, we get: 16 x 82x = 24 x (23)2x
Using rules of indices: (23)2x = 23 x 2x = 26x
Hence, 16 × 82x = 24 x 26x = 24+6x

Answered by Sophie L. Maths tutor

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