Answer:
m = 1, n = 0
Step-by-step explanation:
Given the division expression,
[tex]5^{m}[/tex] ÷ [tex]5^{n}[/tex] = 5
Using the Zero Exponent Rule, [tex]a^{0} = 1[/tex], which essentially means that any nonzero number raised to zero equal to 1. We should apply this property to the divisor, [tex]5^{n}[/tex], so that you get a quotient of 1. Doing so leaves you with:
[tex]5^{m}[/tex] ÷ [tex]5^{0}[/tex] = [tex]5^{m}[/tex] ÷ 1 = 5
This makes it easier to determine that the value of m = 1, because raising a number to an exponent of 1 results to the same number. In other words, [tex]5^{1} = 5[/tex].
Therefore: [tex]5^{m}[/tex] ÷ [tex]5^{n}[/tex] = [tex]5^{1}[/tex] ÷ [tex]5^{0}[/tex] = 5 ÷ 1 = 5.
Hence, the correct answers are: m = 1, and n = 0.
