%5E3.jpeg "(-4xy^3)^3")
Simplifying the Expression (-4xy^3)^3
This article will guide you through the process of simplifying the expression (-4xy^3)^3.
Understanding the Exponent Rule
The key to simplifying this expression lies in understanding the power of a product rule: (ab)^n = a^n * b^n. This rule states that raising a product to a power is the same as raising each factor in the product to that power.
Applying the Rule
Let's apply the rule to our expression:
- (-4xy^3)^3 = (-4)^3 * x^3 * (y^3)^3
Now, we can further simplify:
- (-4)^3 = -64
- (y^3)^3 = y^(3*3) = y^9
Final Result
Putting everything together, the simplified form of (-4xy^3)^3 is:
-64x^3y^9
Therefore, the expression has been simplified by applying the power of a product rule and evaluating the powers of individual factors.