(3a5)2

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Jun 07, 2024

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(3a5)2: Understanding Exponents and Algebraic Expressions

In algebra, expressions with exponents play a crucial role in solving equations and simplifying complex mathematical problems. One such expression is (3a5)2, which may seem daunting at first, but with a clear understanding of the rules of exponents, it can be easily simplified.

What does the expression (3a5)2 mean?

The expression (3a5)2 can be broken down into its components:

• 3 is a coefficient, which is a numerical value that is multiplied by the variables.
• a is a variable, which represents an unknown value.
• 5 is an exponent, which is a small number that is raised to a power.
• 2 is an exponent, which is the power to which the expression inside the parentheses is raised.

How to simplify (3a5)2

To simplify the expression (3a5)2, we need to follow the rules of exponents:

1. Distribute the exponent 2 to the expression inside the parentheses: (3a5)2 = (3^2)(a^2)(5^2)
2. Simplify each component:
   • 3^2 = 9
   • a^2 remains as it is, since we cannot simplify further without knowing the value of a.
   • 5^2 = 25

Simplified Expression

Combining the simplified components, we get:

(3a5)2 = 9a^2 × 25 = 225a^2

Conclusion

In conclusion, simplifying the expression (3a5)2 involves applying the rules of exponents, distributing the exponent to the components inside the parentheses, and simplifying each component. By following these steps, we arrive at the simplified expression 225a^2.