Given the expression:
[tex]\frac{r^8\cdot r^{-8}}{4}[/tex]
to simplify, first we must use the following rule for exponents:
[tex]a^n\cdot a^m=a^{n+m}[/tex]
then, in this case we have the following:
[tex]\frac{r^8\cdot r^{-8}}{4}=\frac{r^{8+(-8)}}{4}=\frac{r^{8-8}}{4}=\frac{r^0}{4}[/tex]
now, remember that any number with an exponent 0 is the unit, this means that a^0=1, then:
[tex]\frac{r^0}{4}=\frac{1}{4}[/tex]
therefore, the simplified expression is 1/4
