Answer:
[tex]a= 10,\:\: b=6[/tex]
Step-by-step explanation:
- [tex]\frac{7^2\:.\:7^8}{7^4}=\frac{7^a}{7^4}=7^b[/tex]
- [tex]\rightarrow\frac{7^{2+8}}{7^4}=\frac{7^a}{7^4}=7^b[/tex]
- [tex]\rightarrow\frac{7^{10}}{7^4}=\frac{7^a}{7^4}=7^b[/tex]
- [tex]\rightarrow {7^{10-4}}={7^{a-4}}=7^b[/tex]
- [tex]\rightarrow {7^{6}}={7^{a-4}}=7^b[/tex]
- [tex]\rightarrow 6=a-4=b[/tex] (Bases are equal so exponents will also be equal)
- [tex]\rightarrow 6=a-4,\:\: 6=b[/tex]
- [tex]\rightarrow 6+4=a,\:\: 6=b[/tex]
- [tex]\rightarrow a= 10,\:\: b=6[/tex]
