If 25a2 = 5-1 × 125. Find the value of a?

Analyze the question: The expression "25a2" most likely means 25^(a²) (the "2" lost its superscript formatting). Let's solve it with that reading.

Concept: Write every number as a power of the same base (here 5), then compare the indices.

Solution:

25^(a²) = 5⁻¹ × 125

• Left side: 25^(a²) = (5²)^(a²) = 5^(2a²)
• Right side: 5⁻¹ × 5³ = 5^(3−1) = 5²

So 5^(2a²) = 5², which gives:

2a² = 2 a² = 1 a = ±1

Check the other reading: If it meant 25 × a² literally, then 25a² = 5⁻¹ × 125 = 25, so a² = 1 and a = ±1 as well. Both readings give the same result.

Answer: a = ±1, which is option C.

Tip: When a variable is squared, always remember there are two roots, positive and negative. Options like "a = 1" or "a = -1" alone are usually traps. Also, when you see powers of 5, 25 and 125, convert everything to base 5 first.