(2x^4)^-3

Jasonbradley

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Jun 16, 2024

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Simplifying (2x^4)^-3

This expression involves both exponents and parentheses, so we need to apply the rules of exponents in the correct order. Here's how we simplify it:

Understanding the Rules

• Power of a Product: (ab)^n = a^n * b^n
• Power of a Power: (a^m)^n = a^(m*n)
• Negative Exponent: a^-n = 1/a^n

Step-by-Step Simplification

1. Apply the Power of a Product rule: (2x^4)^-3 = 2^-3 * (x^4)^-3

2. Apply the Power of a Power rule: 2^-3 * (x^4)^-3 = 2^-3 * x^(4*-3) = 2^-3 * x^-12

3. Apply the Negative Exponent rule: 2^-3 * x^-12 = 1/2^3 * 1/x^12

4. Simplify: 1/2^3 * 1/x^12 = 1/8 * 1/x^12 = 1/(8x^12)

Conclusion

Therefore, the simplified form of (2x^4)^-3 is 1/(8x^12).