%5E4-simplified.jpeg "(2x^3)^4 Simplified")
Simplifying (2x^3)^4
In algebra, simplifying expressions is an essential skill to master. One of the most challenging types of expressions to simplify is the one involving exponents. In this article, we will explore how to simplify the expression (2x^3)^4.
Understanding the Expression
Before we dive into simplifying the expression, let's break it down and understand what each part represents.
2x^3is a term with a coefficient of 2, a variablex, and an exponent of 3.- The exponent
4outside the parentheses indicates that the entire expression inside the parentheses is being raised to the power of 4.
Simplifying the Expression
To simplify the expression (2x^3)^4, we need to apply the power rule of exponents, which states that (a^m)^n = a^(mn).
In this case, a = 2x^3 and n = 4. Therefore, we can rewrite the expression as:
(2x^3)^4 = (2^(1))^4 * (x^3)^4
Using the power rule, we can simplify the expression further:
(2^(1))^4 = 2^4 = 16
(x^3)^4 = x^(3*4) = x^12
Now, we can combine the two simplified expressions:
(2x^3)^4 = 16x^12
Final Answer
The simplified expression is 16x^12.
Conclusion
Simplifying expressions involving exponents can be challenging, but by applying the power rule and understanding the properties of exponents, we can break down complex expressions into simpler forms. In this article, we showed how to simplify the expression (2x^3)^4 using the power rule, resulting in the final answer of 16x^12.
