## 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)**.