Answer:
[tex]x=2[/tex]
Step-by-step explanation:
We are given:
[tex]\displaystyle \frac{w^{-x+4}}{w^{-3}}=w^{2x+1}[/tex]
First, by the quotient property:
[tex]w^{(-x+4)-(-3)}=w^{2x+1}[/tex]
Since they both have the same base, their exponents must be equivalent:
[tex](-x+4)-(-3)=2x+1[/tex]
Solve for x. Simplify:
[tex]-x+7=2x+1[/tex]
Therefore:
[tex]3x=6\Rightarrow x=2[/tex]
