Simplifying Exponential Expressions: (x^4)^3 x 2x^4
This article will guide you through simplifying the expression (x^4)^3 x 2x^4. We will use the rules of exponents to break down the expression and arrive at a simplified form.
Understanding the Rules of Exponents
Before we dive into simplification, let's review the relevant rules of exponents:
 Power of a power: (x^m)^n = x^(m*n)
 Product of powers: x^m * x^n = x^(m+n)
Simplifying the Expression

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

Simplify 2x^4: This term is already in its simplest form.

Combine the simplified terms: Now we have: x^12 * 2x^4

Apply the "product of powers" rule: x^12 * 2x^4 = 2x^(12+4) = 2x^8

Express with a positive exponent: Since x^8 is equivalent to 1/x^8, the final simplified expression is: 2/x^8
Conclusion
By applying the rules of exponents, we successfully simplified the expression (x^4)^3 x 2x^4 to 2/x^8. Remember, understanding the rules of exponents is crucial for working with expressions that involve powers.