3 min read Jun 17, 2024

Understanding Exponent Rules: (x^4)^2 = x^12 / x^5

This article explores the simplification of the equation (x^4)^2 = x^12 / x^5 using fundamental exponent rules.

Understanding the Exponent Rules

Before diving into the simplification, let's revisit two key exponent rules:

  1. Power of a power: (x^m)^n = x^(m*n)

    • This rule states that raising a power to another power is equivalent to multiplying the exponents.
  2. Division of powers with the same base: x^m / x^n = x^(m-n)

    • This rule states that dividing powers with the same base is equivalent to subtracting the exponents.

Simplifying the Equation

Now, let's apply these rules to simplify our equation:

  1. Simplify the left side: (x^4)^2 = x^(4*2) = x^8

    • We applied the "power of a power" rule.
  2. Simplify the right side: x^12 / x^5 = x^(12-5) = x^7

    • We applied the "division of powers with the same base" rule.

Verifying the Equation

Therefore, the simplified equation becomes x^8 = x^7. This equation is not true for all values of x, and it's important to understand why.

For example:

  • If x = 2, then x^8 = 256 and x^7 = 128.
  • If x = 0, then both sides are equal to 0.

The equation holds true only for the specific case where x = 1.


Simplifying the equation (x^4)^2 = x^12 / x^5 using exponent rules leads to x^8 = x^7. This equation highlights the importance of understanding exponent rules for accurate simplification. Furthermore, it demonstrates that applying these rules may not always lead to a universally true equation. It's essential to remember that the equation holds true only for specific values of x.

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