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(a^3a^6b^2)^3

2 min read Jun 16, 2024
(a^3a^6b^2)^3

Simplifying the Expression (a^3a^6b^2)^3

This article will guide you through simplifying the expression (a^3a^6b^2)^3.

Understanding the Properties

To simplify this expression, we need to understand some key properties of exponents:

  • Product of Powers: When multiplying powers with the same base, we add the exponents. For example, a^m * a^n = a^(m+n)
  • Power of a Power: When raising a power to another power, we multiply the exponents. For example, (a^m)^n = a^(m*n)

Step-by-Step Simplification

  1. Combine terms inside the parentheses:

    • Using the product of powers rule, we combine a^3 and a^6: a^3a^6 = a^(3+6) = a^9.
    • This gives us (a^9b^2)^3

  2. Apply the power of a power rule:

    • We distribute the exponent 3 to both a^9 and b^2: (a^9b^2)^3 = a^(93)b^(23)

  3. Simplify the exponents:

    • a^(9*3) = a^27
    • b^(2*3) = b^6

  4. Final Expression:

    • Therefore, the simplified expression is a^27b^6.

Summary

By applying the properties of exponents, we have successfully simplified the expression (a^3a^6b^2)^3 to a^27b^6.

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