Answer:
[tex]f(x)=-7x+7[/tex]
Step-by-step explanation:
we begin with the expression [tex]\frac{5^{-4x+7} }{125^x}[/tex]
We need to manipulate this expression so that it is in the form of [tex]5^{f(x)}[/tex]
The first thing that we can do with this expression is simplify the denominator. As [tex]125=5^3[/tex], we can rewrite it as
[tex]\frac{5^{-4x+7} }{5^{3x} }[/tex]
Now, we need to recall a property of exponents.
When we divide two numbers with the same base that have exponents, we simply need to subtract the denominator's power from the numerator.
This gives us
[tex]5^{-7x+7}[/tex]
As our expression is in the required form, we now know that [tex]f(x)=-7x+7[/tex]
