%5E3.jpeg "(-5q^2p)^3")
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 non-negative 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.