Answer:
[tex]5^{10} \cdot 5^{-7} = 5^3[/tex]
[tex]\frac{5^{10}}{5^{-7}} = 5^{17}[/tex]
Step-by-step explanation:
You have two equations:
[tex]5^a \cdot 5^b = 5^3[/tex]
[tex]\frac{5^a}{5^b} = 5^{17}[/tex]
But since
[tex]x^a \cdot x^b = x^{a+b}[/tex]
you only need to solve a+b = 3 and a-b=17
Rewrite the second as a = 17+b and plug it into the first:
17+b + b = 3, then you find, 2b = -14, so b = -7.
Then a=3-b, so a = 10.
