2 min read Jun 17, 2024

Understanding (x^2y^3)^4

This expression involves exponents and power of a product. Let's break it down step-by-step.

Exponents Explained

  • Base: The base is the number or variable being multiplied by itself. In this case, the bases are x and y.
  • Exponent: The exponent tells you how many times to multiply the base by itself. Here, we have 2 and 3 as exponents for x and y, respectively.
  • Power: The entire expression (x^2y^3) is raised to the power of 4. This means we are multiplying the entire expression by itself four times.

Applying the Rules

To simplify this, we use the following rules:

1. Power of a Product: When raising a product to a power, you raise each factor to that power.

  • (x^2y^3)^4 = (x^2)^4 * (y^3)^4

2. Power of a Power: When raising a power to another power, you multiply the exponents.

  • (x^2)^4 = x^(2*4) = x^8
  • (y^3)^4 = y^(3*4) = y^12

Therefore, the simplified expression is:

(x^2y^3)^4 = x^8y^12

In Conclusion

Simplifying (x^2y^3)^4 is a straightforward process using the basic rules of exponents. By applying the power of a product and power of a power rules, we arrive at the simplified form x^8y^12.

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