3%E2%8B%85(b2c2).jpeg "(a2b)3⋅(b2c2)")
(a2b)3⋅(b2c2): Understanding the Expression
In algebra, expressions involving variables and constants are commonly used to represent mathematical relationships. One such expression is (a2b)3⋅(b2c2). In this article, we will break down this expression and explore its meaning and significance.
Understanding the Expression
The expression (a2b)3⋅(b2c2) can be understood by breaking it down into its components.
(a2b)3
The expression (a2b)3 means "a squared, b, cubed". This can be expanded as:
(a2b)3 = (a2b) × (a2b) × (a2b)
Using the associative property of multiplication, this can be simplified to:
(a2b)3 = a6b3
(b2c2)
The expression (b2c2) is a simple product of two terms:
(b2c2) = b2 × c2
Combining the Expressions
Now, let's combine the two expressions using the multiplication operator:
(a2b)3⋅(b2c2) = (a6b3) × (b2c2)
Using the commutative property of multiplication, we can rearrange the terms to get:
(a2b)3⋅(b2c2) = a6b5c2
Simplifying the Expression
The final simplified form of the expression is:
(a2b)3⋅(b2c2) = a6b5c2
This expression represents the product of three variables, a, b, and c, with specific exponents.
Conclusion
In conclusion, the expression (a2b)3⋅(b2c2) can be broken down into its components and simplified to a6b5c2. Understanding the rules of algebraic expressions, such as the associative and commutative properties of multiplication, is crucial in simplifying complex expressions like this one.
