### Home > PC > Chapter 6 > Lesson 6.1.3 > Problem6-46

6-46.

Rewrite $f(x)=27(9)^{\frac{1}{2}x-1}$ in $f(x)=ab^x$ form. Show all of your steps in the process!

Change the $27$ and the $9$ to numbers with base $3$.

$f(x)=3^{3}(3^2)^{\left(x/2-1\right)}$

Use the power to a power property of exponents.

$f(x)=3^3(3)^{x-2}$

Use the multiplication property of exponents.

$f(x)=(3)^{3+x−2}$

Simplify.

$f(x)=(3)^{x+1}$

Put in the $ab^x$ form.

$f(x)=3(3)^x$