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(x^4)^2=x^12/x^5 (x Khác 0)

2 min read Jun 17, 2024
(x^4)^2=x^12/x^5 (x Khác 0)

Simplifying Expressions with Exponents

This article will explore the simplification of the expression (x^4)^2 = x^12 / x^5 where x is not equal to 0.

Understanding the Properties of Exponents

The problem involves two key properties of exponents:

  • Power of a power: (x^m)^n = x^(m*n)
  • Division of powers with the same base: x^m / x^n = x^(m-n)

Simplifying the Expression

Let's break down the simplification step-by-step:

  1. Simplify the left side: (x^4)^2 = x^(4*2) = x^8
  2. Simplify the right side: x^12 / x^5 = x^(12-5) = x^7

Now we have: x^8 = x^7.

Note: For this equation to be true, x must be equal to 1. This is because any number raised to the power of 8 will be greater than the same number raised to the power of 7 unless that number is 1.

Conclusion

The expression (x^4)^2 = x^12 / x^5 simplifies to x^8 = x^7. This equation holds true only when x = 1. The key to solving this type of problem is understanding and applying the basic properties of exponents.

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