%5E2.jpeg "(2ab^3)^2")
(2ab^3)^2: Understanding the Exponentiation
In algebra, exponentiation is a fundamental operation that involves raising a number or expression to a power. In this article, we will explore the concept of exponentiation using the example of (2ab^3)^2.
What is Exponentiation?
Exponentiation is a mathematical operation that involves raising a number or expression to a power. It is denoted by a superscript number, which indicates the power to which the base number or expression should be raised. For example, in the expression a^n, a is the base and n is the exponent.
The Expression (2ab^3)^2
Now, let's consider the expression (2ab^3)^2. Here, we have a combination of two expressions: 2ab^3 and ^2. To evaluate this expression, we need to follow the order of operations (PEMDAS):
- Evaluate the expression inside the parentheses:
2ab^3 - Raise the result to the power of 2:
(2ab^3)^2
Evaluating the Expression
To evaluate the expression 2ab^3, we need to follow the order of operations:
- Raise
bto the power of 3:b^3 - Multiply
2andawithb^3:2ab^3
Now, we have the result: 2ab^3. To raise this expression to the power of 2, we need to multiply it by itself:
(2ab^3)^2 = (2ab^3)(2ab^3)
Simplifying the Expression
To simplify the expression, we can use the exponentiation rule: (a^m)^n = a^(mn). In this case, we have:
(2ab^3)^2 = 2^2(a^2)(b^6)
= 4a^2b^6
Therefore, the final result of the expression (2ab^3)^2 is 4a^2b^6.
Conclusion
In this article, we have explored the concept of exponentiation using the example of (2ab^3)^2. We have seen how to evaluate the expression by following the order of operations and simplifying the result using the exponentiation rule. Understanding exponentiation is essential in algebra and other branches of mathematics, and we hope this article has helped you to grasp this important concept.
