%5E5-simplified.jpeg "(3m^2n^7/m)^5 Simplified")
Simplifying the Expression (3m^2n^7/m)^5
This article will guide you through simplifying the expression (3m^2n^7/m)^5. We will use the rules of exponents to break down the expression step by step.
Understanding the Rules of Exponents
Before we begin simplifying, let's review the relevant rules of exponents:
- Product of powers: x^m * x^n = x^(m+n)
- Quotient of powers: x^m / x^n = x^(m-n)
- Power of a product: (xy)^n = x^n * y^n
- Power of a quotient: (x/y)^n = x^n / y^n
- Power of a power: (x^m)^n = x^(m*n)
Simplifying the Expression
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Distribute the exponent: Using the power of a quotient rule, we can rewrite the expression as: (3m^2n^7/m)^5 = (3^5 * (m^2)^5 * (n^7)^5) / (m^5)
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Simplify the exponents: Applying the power of a power rule: (3^5 * (m^2)^5 * (n^7)^5) / (m^5) = (243 * m^10 * n^35) / (m^5)
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Simplify the terms: Using the quotient of powers rule: (243 * m^10 * n^35) / (m^5) = 243 * m^(10-5) * n^35
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Final simplified expression: 243 * m^(10-5) * n^35 = 243m^5n^35
Conclusion
By applying the rules of exponents, we have successfully simplified the expression (3m^2n^7/m)^5 to 243m^5n^35. Remember to always follow the order of operations and use the appropriate rules for each step.