Question

3² x 3^-4 x 3⁵ is equal to :

• A. 3^3
• B. 3^2
• C. 3^5
• D. 3

Answer 1

Answer:

A. 3^3

Laws of Exponents

• When multiplying terms with the same base, you add their exponents. This is based on the law: a^m × aⁿ = a^m+n.
• In this problem, we have the expression 3² × 3^-4 × 3⁵.
• All terms have the same base, which is 3.
• According to the law of exponents, we add the powers: 2 + (-4) + 5.
• Calculating the sum of the exponents: 2 - 4 + 5 = -2 + 5 = 3.
• Therefore, the expression simplifies to 3³.

Background on Exponents

• An exponent indicates how many times a base number is multiplied by itself.
• For example, in 3², 3 is the base and 2 is the exponent. It means 3 × 3.
• A negative exponent, such as in 3^-4, means the reciprocal of the base raised to the positive exponent. So, 3^-4 = 1/3⁴.
• This property of exponents is fundamental in algebra and is frequently tested in competitive exams.