%5E2.jpeg "(10a^7b^2c^6)^2")
Simplifying Expressions with Exponents: (10a^7b^2c^6)^2
In mathematics, simplifying expressions with exponents often involves applying the rules of exponents. Let's explore how to simplify the expression (10a^7b^2c^6)^2.
Understanding the Rules
- Power of a product: (ab)^n = a^n * b^n
- Power of a power: (a^m)^n = a^(m*n)
Applying the Rules
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Distribute the exponent: We begin by applying the power of a product rule to the entire expression. This means squaring each term inside the parentheses:
(10a^7b^2c^6)^2 = 10^2 * (a^7)^2 * (b^2)^2 * (c^6)^2
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Simplify the exponents: Now, we apply the power of a power rule to each term:
10^2 * (a^7)^2 * (b^2)^2 * (c^6)^2 = 100 * a^(72) * b^(22) * c^(6*2)
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Final simplification: Perform the multiplication in the exponents:
100 * a^(72) * b^(22) * c^(6*2) = 100a^14b^4c^12
Conclusion
Therefore, the simplified form of (10a^7b^2c^6)^2 is 100a^14b^4c^12. By understanding and applying the rules of exponents, we can effectively simplify complex expressions.