Question

How do you rewrite `y = 4(3)^(2x+2)` in `y = a * b^x` form?

Answer 1

`y=4*3^(2x+2)=36*9^x`

with:

`a=36`
`b=9`

Explanation:

Remembering that:

`a^(p+q)=a^p*a^q`

`(a^n)^m=a^(n*m)`

then:

`y=4*3^(2x+2)=4*3^(2x)*3^2=`
`=4*9*(3^2)^x=36*9^x`

Answer 2

`y=4(3)^(2x+2)hArr y=36*9^x`

Explanation:

`4(3)^(2x+2)`

`color(white)("XXX")=4*((3^2)^(x+1))`

`color(white)("XXX")=4*(9^(x+1))`

`color(white)("XXX")=4*(9*9^x)`

`color(white)("XXX")=4*9*(9^x)`

`color(white)("XXX")=36*9^x`