%5E3.jpeg "(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
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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
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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)
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Simplify the exponents:
- a^(9*3) = a^27
- b^(2*3) = b^6
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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.