(2a^2b^4)^3/4a^3b^7

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (2a^2b^4)^3 / 4a^3b^7

This article will guide you through simplifying the given expression: (2a^2b^4)^3 / 4a^3b^7.

Understanding the Rules

To simplify this expression, we'll need to apply a few fundamental rules of exponents:

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

Step-by-Step Solution

1. Simplify the numerator:

   • Apply the power of a product rule: (2a^2b^4)^3 = 2^3 * (a^2)^3 * (b^4)^3
   • Apply the power of a power rule: 2^3 * (a^2)^3 * (b^4)^3 = 8a^6b^12

2. Rewrite the entire expression: Now our expression becomes: 8a^6b^12 / 4a^3b^7

3. Simplify by dividing:

   • Apply the division of powers with the same base rule: 8a^6b^12 / 4a^3b^7 = (8/4) * a^(6-3) * b^(12-7)

4. Final Simplification:

   • (8/4) * a^(6-3) * b^(12-7) = 2a^3b^5

Conclusion

Therefore, the simplified form of the expression (2a^2b^4)^3 / 4a^3b^7 is 2a^3b^5. Remember to apply the exponent rules carefully and step-by-step to achieve the correct answer.