So the ultimate goal is to get to 1/5, aka 5^(-1)
First option: [tex]\frac{5^5}{1} * \frac{5^7}{1} *\frac{1}{5^{13}}= \frac{5^{12}}{5^{13}}=5^{-1}= \frac{1}{5} [/tex]
Second option: [tex]5^5*5^7*5^{-13}=5^{-1}= \frac{1}{5} [/tex]
Third option: [tex] \frac{5^{12}}{5^{13}}=5^{-1}= \frac{1}{5} [/tex]
Fourth option: [tex] \frac{5^5*5^7}{5^{13}} = \frac{5^{12}}{5^{13}}=5^{-1}= \frac{1}{5} [/tex]
To summarize, all the options are correct.
