Simplifying the Expression: (x^4)^3 * 2x^4
This article will guide you through simplifying the expression (x^4)^3 * 2x^4. We'll break down the steps using the rules of exponents.
Understanding the Rules of Exponents
Before we begin simplifying, let's recall some key rules of exponents:
 Product of Powers: x^m * x^n = x^(m+n)
 Power of a Power: (x^m)^n = x^(m*n)
 Negative Exponent: x^n = 1/x^n
Simplifying the Expression

Simplify (x^4)^3: Applying the "Power of a Power" rule, we get: (x^4)^3 = x^(4*3) = x^12

Rewrite x^12 using the "Negative Exponent" rule: x^12 = 1/x^12

Substitute the simplified terms back into the original expression: (x^4)^3 * 2x^4 = (1/x^12) * 2x^4

Apply the "Product of Powers" rule: (1/x^12) * 2x^4 = 2 * (x^4 / x^12) = 2x^(412) = 2x^8

Rewrite the expression using the "Negative Exponent" rule: 2x^8 = 2/x^8
Conclusion
Therefore, the simplified form of the expression (x^4)^3 * 2x^4 is 2/x^8.