UGC NET Questions (Paper – 1)

When multiplying powers of the same base, we keep the base unchanged and add the exponents. The expression 3⁴ × 3² therefore becomes 3^(4 + 2). Adding the exponents gives 3⁶. This rule arises directly from expanding each power into repeated multiplication and then counting the total number of factors of 3.

Option A:
Option A, 3⁸, results from incorrectly multiplying the exponents instead of adding them. There is no exponent law that justifies multiplying 4 and 2 in this context.

Option B:
Option B correctly applies the exponent rule aᵐ × aⁿ = aᵐ⁺ⁿ. By adding 4 and 2, it expresses the product as a single power of 3 with exponent 6.

Option C:
Option C, 3², keeps only one of the original exponents and discards the contribution of the other factor. This contradicts the idea of combining powers.

Option D:
Option D, 3⁴, similarly ignores the factor 3² and so cannot be equivalent to the full product.