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Simplifying Exponential Expressions: (m^5n^3)^7 x^2n
This article will guide you through simplifying the expression (m^5n^3)^7 x^2n. We'll break down the steps using the rules of exponents.
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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Simplify the first term: (m^5n^3)^7
- Apply the "power of a product" rule: (m^5n^3)^7 = (m^5)^7 * (n^3)^7
- Apply the "power of a power" rule: (m^5)^7 * (n^3)^7 = m^(57) * n^(37) = m^35 * n^21
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Combine the simplified first term with the second term:
- Now we have: m^35 * n^21 * x^2n
The Simplified Expression
Therefore, the simplified form of the expression (m^5n^3)^7 x^2n is m^35 * n^21 * x^2n.
Key Takeaways
- When simplifying expressions with exponents, remember the fundamental rules.
- Break down complex expressions into smaller parts for easier manipulation.
- Always strive to present your answer in the most simplified form.