Express 8^(2x+3) in the form  2^y , stating y in terms of x.

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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we know that `8 = 2^3`

Further we know the following rule regarding indices.

`(a^b)^(c) = a^(bc)`

 

So we can write `8^(2x+3) ` as;

`(2^3)^(2x+3)`

`= 2^(3(2x+3))`

`= 2^(6x+9)`

 

So finally

`2^(6x+9) = 2^y ` where `y = 6x+9`

 

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