Simplifying Expressions with Exponents
Let's explore how to simplify the expression (5a²bc³)(1/5 abc⁴).
Understanding the Basics
 Exponents: The small numbers written above and to the right of variables (like the "2" in a²) represent the number of times that variable is multiplied by itself.
 Multiplication: When multiplying terms with exponents and the same base, we add the exponents. For example, a² * a³ = a^(2+3) = a⁵.
Simplifying the Expression

Rearrange the terms:
(5a²bc³)(1/5 abc⁴) = (5 * 1/5) * (a² * a) * (b * b) * (c³ * c⁴) 
Simplify the coefficients: (5 * 1/5) = 1

Apply exponent rules for variables:
 a² * a = a^(2+1) = a³
 b * b = b²
 c³ * c⁴ = c^(3+4) = c⁷

Combine the simplified terms: 1 * a³ * b² * c⁷ = a³b²c⁷
Conclusion
Therefore, the simplified form of (5a²bc³)(1/5 abc⁴) is a³b²c⁷. Remember, when working with expressions involving exponents, the key is to apply the rules of exponents systematically to arrive at the most simplified form.