%5E3-simplified.jpeg "(4x^3)^3 Simplified")
Simplifying Exponents: (4x^3)^3
When working with exponents, it's essential to understand the rules of exponentiation. One of the most common rules is the power of a power, which states that when an expression with an exponent is raised to another power, we multiply the exponents. In this article, we'll explore how to simplify the expression (4x^3)^3.
Step 1: Multiply the Exponents
To simplify the expression (4x^3)^3, we need to multiply the exponent 3 by the exponent outside the parentheses. Remember, when we multiply exponents, we add them together.
(4x^3)^3 = 4^(3*1) * x^(3*3)
Step 2: Evaluate the Exponents
Now, let's evaluate the exponents:
4^(3*1) = 4^3 = 64
x^(3*3) = x^9
Step 3: Simplify the Expression
Combining the results from Steps 1 and 2, we get:
(4x^3)^3 = 64x^9
And that's the simplified result!
Conclusion
Simplifying exponents can be straightforward when you understand the rules of exponentiation. By multiplying the exponents and evaluating the results, we can simplify complex expressions like (4x^3)^3 to get the simplified result 64x^9. Remember to follow the order of operations and apply the rules of exponentiation to simplify expressions with ease.
