Question

There are parts A and B.a) Find two numbers m and n that satisfy the equationb) Describe the number of solutions that satisfy the equation. Explain your reasoning.

Answer 1

When we have a quotient of powers in the form

$\frac{a^m}{a^n}$

since both of them have the same base, this means that we can rewrite as a single power in the form

$a^{m-n}$

for that reason:

Part A:

Any numbers that have a difference of 2 can be possible numbers for m and n,

then m=5 and n=3 are two possible numbers that satisfy the equation

Part B:

There are many pairs of numbers that have a difference of two, like 10 and 8, 19 and 17, 7 and 5, and so on... this means that there are infinitely many solutions that satisfy an equation from the difference in the exponents.

$m-n=2$