%5E5-simplify.jpeg "(2x^3)^5 Simplify")
Simplifying (2x^3)^5
In algebra, simplifying expressions is an essential skill to master. One of the common expressions that students struggle with is (2x^3)^5. In this article, we will break down the steps to simplify this expression.
Using the Power Rule
The power rule of exponents states that when we raise a power to another power, we multiply the exponents. Mathematically, this can be written as:
(a^m)^n = a^(mn)
In our case, we have (2x^3)^5. Here, a = 2x^3, m = 3, and n = 5.
Applying the Power Rule
Using the power rule, we can rewrite the expression as:
(2x^3)^5 = 2^(35) * x^(35) = 2^15 * x^15** = 2^15x^15
Simplifying the Expression
The final answer is 2^15x^15. We can see that the expression is simplified, and we have got rid of the parentheses.
Conclusion
Simplifying (2x^3)^5 is a straightforward process when we apply the power rule of exponents. By multiplying the exponents, we can rewrite the expression in a more compact form. In this case, the simplified expression is 2^15x^15.
