%5E3.jpeg "(5a^2)^3")
Simplifying (5a^2)^3
In mathematics, simplifying expressions is a crucial skill. Let's break down how to simplify the expression (5a^2)^3.
Understanding the Concept
The expression (5a^2)^3 represents the product of (5a^2) multiplied by itself three times:
(5a^2)^3 = (5a^2) * (5a^2) * (5a^2)
Applying the Rules of Exponents
To simplify, we need to apply the following rules of exponents:
- Product of powers: (x^m)^n = x^(m*n)
Applying the Rules to the Expression
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Distribute the exponent: Apply the product of powers rule to both the coefficient (5) and the variable (a^2): (5a^2)^3 = 5^3 * (a^2)^3
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Simplify the exponents: 5^3 * (a^2)^3 = 125 * a^(2*3)
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Final simplification: 125 * a^(2*3) = 125a^6
Conclusion
Therefore, the simplified form of (5a^2)^3 is 125a^6.