%5E3-simplify.jpeg "(a^2b^4c)^3 Simplify")
Simplifying Expressions with Exponents: (a²b⁴c)³
In mathematics, simplifying expressions often involves understanding and applying the rules of exponents. One common type of simplification involves expressions raised to a power, such as (a²b⁴c)³. Let's break down how to simplify this expression.
Understanding the Rules of Exponents
The key rule we'll use here is the power of a product rule:
(xy)ⁿ = xⁿyⁿ
This rule states that when a product is raised to a power, each factor in the product is raised to that power.
Simplifying the Expression
-
Apply the power of a product rule:
(a²b⁴c)³ = a²³ * b⁴³ * c³
-
Simplify the exponents:
a²³ * b⁴³ * c³ = a⁶ * b¹² * c³
Final Result
Therefore, the simplified expression for (a²b⁴c)³ is a⁶b¹²c³.
Key Takeaway
Remember that the power of a product rule allows you to distribute the exponent to each factor within the parentheses. This simplification process can be applied to various expressions involving exponents and products.