-to-the-power-of-2.jpeg "(2x To The Power Of 3) To The Power Of 2")
Understanding (2x³)²
In mathematics, expressions like (2x³)² can seem confusing at first glance. However, with a clear understanding of the rules of exponents, they become quite simple to solve.
Breaking Down the Expression
The expression (2x³)² represents the square of the entire term 2x³. Let's break it down:
- 2x³: This part involves multiplying the variable 'x' by itself three times (x³) and then multiplying the result by 2.
- ²: This exponent indicates that we need to multiply the entire term (2x³) by itself.
Applying the Rules of Exponents
To solve this expression, we need to apply the following rules:
- Power of a product: (ab)^n = a^n * b^n
- Power of a power: (a^m)^n = a^(m*n)
Solving the Expression
Using these rules, we can rewrite and solve the expression as follows:
- Apply the power of a product rule: (2x³)² = 2² * (x³)²
- Apply the power of a power rule: 2² * (x³)² = 4 * x⁶
Final Result
Therefore, (2x³)² simplifies to 4x⁶.
Key Takeaways
- Understanding the rules of exponents is crucial for solving these types of expressions.
- Remember to apply the rules in the correct order to achieve the correct simplification.
- Always check your work to ensure accuracy.