Question

If a³⁰ = (aᵐ)ⁿ, which of the following could be values for m and n?

a) m = -5, n = 10
b) m = 0, n = 30
c) m = -6, n = -5
d) m = 5, n = 25

Answer 1

The pair that satisfies the condition a³⁰ = (aᵐ)ⁿ, where m times n equals 30, is (m = -6, n = -5).

Step-by-step explanation:

The student's question asks about the properties of exponentiation, specifically when a³⁰ equals (aᵐ)ⁿ, and which pairs of values for m and n satisfy this equation. To solve this problem, we use the law of exponents which states that (aʸⁿ) = aⁿʸ. Therefore, we are looking for values of m and n such that m times n equals 30.

• m = -5, n = 10: This is a correct pair because (-5)×10 = -50, which does not equal 30.
• m = 0, n = 30: This does not work because 0×30 = 0, not 30.
• m = -6, n = -5: This pair is also incorrect because (-6)×(-5) = 30, satisfying the original condition.
• m = 5, n = 25: This is the correct pair since 5×25 = 125, which does not equal 30.

Therefore, the pair (m, n) that could be the values satisfying the original condition is (m = -6, n = -5).