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(3^5)^2/3^-2

2 min read Jun 16, 2024
(3^5)^2/3^-2

Simplifying Exponents: (3^5)^2 / 3^-2

This problem involves simplifying an expression with exponents. Here's a step-by-step explanation:

Understanding the Rules of Exponents

  • Power of a power: When raising a power to another power, you multiply the exponents. For example, (x^m)^n = x^(m*n)
  • Negative exponent: A negative exponent indicates a reciprocal. For example, x^-n = 1/x^n

Applying the Rules

  1. Simplify the numerator: (3^5)^2 = 3^(5*2) = 3^10

  2. Simplify the denominator: 3^-2 = 1/3^2

  3. Rewrite the expression: Now the expression becomes 3^10 / (1/3^2)

  4. Dividing by a fraction: Dividing by a fraction is the same as multiplying by its reciprocal. So, 3^10 / (1/3^2) = 3^10 * 3^2

  5. Multiplying exponents with the same base: When multiplying exponents with the same base, you add the powers. So, 3^10 * 3^2 = 3^(10+2) = 3^12

The Answer

Therefore, the simplified expression of (3^5)^2 / 3^-2 is 3^12.

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