Answer:
n= 4
Step-by-step explanation:
[tex]a^{m}*a^{n}=a^{m+n}\\\\(a^{m})^{n}=a^{m*n}\\\\\frac{a^{m}}{a^{n}}=a^{m-n}[/tex]
[tex]7^{7}*7^{5}=\frac{(7^{n})^{4}}{7^{4}}\\\\7^{7+5}=\frac{7^{n*4}}{7^{4}}\\\\7^{12}=\frac{7^{4n}}{7^{4}}\\\\7^{12}=7^{4n-4}[/tex]
Compare the exponents,
4n - 4 = 12 {Add 4 to both sides}
4n = 12 + 4
4n = 16
n = 16/4
n = 4
