## 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.