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(ab^2)^3/b^5

2 min read Jun 16, 2024
(ab^2)^3/b^5

Simplifying Expressions: (ab^2)^3 / b^5

This article will guide you through simplifying the expression (ab^2)^3 / b^5.

Understanding the Rules

To simplify this expression, we need to apply some basic 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 Simplification

  1. Apply the power of a product rule to the numerator: (ab^2)^3 = a^3 * (b^2)^3

  2. Apply the power of a power rule to the numerator: a^3 * (b^2)^3 = a^3 * b^(2*3) = a^3 * b^6

  3. Rewrite the expression with the simplified numerator: (a^3 * b^6) / b^5

  4. Apply the division of powers with the same base rule: a^3 * b^(6-5) = a^3 * b^1

  5. Simplify: a^3 * b

Conclusion

Therefore, the simplified form of the expression (ab^2)^3 / b^5 is a^3 * b.

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