Simplifying (5q^2p)^3
This expression involves raising a monomial to a power. Let's break down how to simplify it:
Understanding the Basics
 Monomial: A monomial is a single term expression consisting of a coefficient and variables with nonnegative integer exponents. In our case, (5q²p) is a monomial.
 Exponents: An exponent indicates how many times a base is multiplied by itself. Here, 3 is the exponent, meaning we multiply (5q²p) by itself three times.
The Process
To simplify (5q²p)³, we apply the following rules of exponents:

Distribute the exponent: When raising a product to a power, we raise each factor within the parentheses to that power.
 (5q²p)³ = (5)³ * (q²)³ * (p)³

Simplify each factor:
 (5)³ = 125
 (q²)³ = q⁶ (applying the rule (a^m)^n = a^(m*n))
 (p)³ = p³

Combine the results:
 (5q²p)³ = 125q⁶p³
Therefore, the simplified form of (5q²p)³ is 125q⁶p³.
Key Points
 Remember to distribute the exponent to each factor within the parentheses.
 Apply the rule of exponents when raising a power to another power.
 Pay attention to the sign of the coefficient, as a negative coefficient raised to an odd power remains negative.