%5E3.jpeg "(-3ab^4)^3")
Simplifying (-3ab^4)^3
This article will guide you through the process of simplifying the expression (-3ab^4)^3. We will break down the steps and explain the rules of exponents involved.
Understanding the Properties of Exponents
Before we begin, let's refresh our memory on the key properties of exponents:
- Product of powers: x^m * x^n = x^(m+n)
- Power of a power: (x^m)^n = x^(m*n)
- Power of a product: (x*y)^n = x^n * y^n
Step-by-Step Simplification
-
Apply the power of a product rule:
(-3ab^4)^3 = (-3)^3 * a^3 * (b^4)^3
-
Apply the power of a power rule:
(-3)^3 * a^3 * (b^4)^3 = -27 * a^3 * b^(4*3)
-
Simplify:
-27 * a^3 * b^(4*3) = -27a^3b^12
Final Answer
Therefore, the simplified form of (-3ab^4)^3 is -27a^3b^12.
Key Takeaways
Remember to apply the properties of exponents correctly to simplify expressions like this. The power of a product rule and the power of a power rule are crucial for dealing with exponents raised to other exponents.