(a^4b^0/5a^-2b^3)^2

2 min read Jun 16, 2024
(a^4b^0/5a^-2b^3)^2

Simplifying the Expression: (a^4b^0/5a^-2b^3)^2

This expression involves several rules of exponents and fractions. Let's break it down step by step:

Understanding the Rules

  • Anything to the power of 0 equals 1: b^0 = 1
  • Negative exponents in the denominator become positive in the numerator: a^-2 = 1/a^2
  • When dividing exponents with the same base, subtract the powers: a^4 / a^-2 = a^(4-(-2)) = a^6
  • When raising a power to another power, multiply the exponents: (a^m)^n = a^(m*n)

Simplifying the Expression

  1. Apply the rule for exponents of 0: (a^4 * 1 / 5a^-2b^3)^2
  2. Apply the rule for negative exponents: (a^4 * 1 / (5 * 1/a^2 * b^3))^2
  3. Simplify the denominator: (a^4 / (5/a^2 * b^3))^2
  4. Apply the rule for dividing exponents with the same base: (a^(4+2) / 5b^3)^2
  5. Simplify the numerator: (a^6 / 5b^3)^2
  6. Apply the rule for raising a power to another power: a^(6*2) / (5b^3)^2
  7. Simplify further: a^12 / (25b^6)

Final Result

Therefore, the simplified expression for (a^4b^0/5a^-2b^3)^2 is a^12 / (25b^6).

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