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(2x^4y^7)^3

2 min read Jun 16, 2024
(2x^4y^7)^3

Simplifying (2x^4y^7)^3

This expression involves the power of a product and requires careful application of exponent rules. Let's break down the process step-by-step.

Understanding the Exponent Rules

  • Power of a product: (ab)^n = a^n * b^n
  • Power of a power: (a^m)^n = a^(m*n)

Applying the Rules

  1. Distribute the exponent: Since we have a product (2x^4y^7) raised to the power of 3, we can apply the power of a product rule. This gives us:

    (2x^4y^7)^3 = 2^3 * (x^4)^3 * (y^7)^3

  2. Simplify the powers: Now we apply the power of a power rule to each individual term:

    2^3 * (x^4)^3 * (y^7)^3 = 8 * x^(43) * y^(73)

  3. Final result: This simplifies to:

    8 * x^(43) * y^(73) = 8x^12y^21

Conclusion

Therefore, the simplified form of (2x^4y^7)^3 is 8x^12y^21.

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