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

2 min read Jun 17, 2024
(x^4)^-3 Times 2x^4

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

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

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

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

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

  5. 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.

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