(x^4)^-3 X 2x^4

Jasonbradley

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Jun 17, 2024

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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

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

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

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

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

5. 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.