%5E2(x%5E3).jpeg "(8x^4)^2(x^3)")
Simplifying the Expression (8x^4)^2(x^3)
This expression involves a combination of exponents and multiplication. To simplify it, we need to apply the rules of exponents.
1. Understanding the Rules of Exponents:
- Power of a Power: (a^m)^n = a^(m*n)
- Product of Powers: a^m * a^n = a^(m+n)
2. Simplifying the Expression:
Let's break down the simplification step by step:
- (8x^4)^2: Using the power of a power rule, we get 8^2 * (x^4)^2 = 64x^8
- 64x^8 * x^3: Now, using the product of powers rule, we get 64x^(8+3) = 64x^11
3. Final Result:
Therefore, the simplified form of (8x^4)^2(x^3) is 64x^11.
Important Note: Always remember to apply the rules of exponents correctly. Understanding the power of a power rule and the product of powers rule is crucial for simplifying expressions involving exponents.