%5E2.jpeg "(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
- Apply the rule for exponents of 0: (a^4 * 1 / 5a^-2b^3)^2
- Apply the rule for negative exponents: (a^4 * 1 / (5 * 1/a^2 * b^3))^2
- Simplify the denominator: (a^4 / (5/a^2 * b^3))^2
- Apply the rule for dividing exponents with the same base: (a^(4+2) / 5b^3)^2
- Simplify the numerator: (a^6 / 5b^3)^2
- Apply the rule for raising a power to another power: a^(6*2) / (5b^3)^2
- 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).