%5E3.jpeg "(4x^4 X^4)^3")
Simplifying (4x^4 * x^4)^3
This expression involves several key concepts in algebra, including exponents, multiplication, and order of operations. Let's break it down step by step:
1. Simplifying the Base
- Combine like terms: Within the parentheses, we have 4x^4 multiplied by x^4. Since the bases are the same (x), we can add the exponents:
- 4x^4 * x^4 = 4x^(4+4) = 4x^8
- Our expression now becomes: (4x^8)^3
2. Applying the Power of a Power Rule
- The rule: (a^m)^n = a^(m*n)
- Applying the rule: In our case, a = 4x, m = 8, and n = 3.
- Result: (4x^8)^3 = 4^(83) * x^(83) = 4^24 * x^24
3. Final Result
The simplified form of (4x^4 * x^4)^3 is 4^24 * x^24.
Important Note: 4^24 is a very large number. You could leave it in this form, or calculate the actual value if needed.