Find the value of m for which 5^m ÷5⁻³ = 5⁵.

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Solution

5^m ÷ 5⁻³ = 5⁵

5^m ^{− (− 3)} = 5⁵ (a^m ÷ aⁿ = a^m⁻ⁿ)

5^m^{+ 3} = 5⁵

Since the powers have same bases on both sides, their respective exponents must be equal.

m + 3 = 5

m = 5 − 3

m = 2

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