%5E7*m%5E2n.jpeg "(m^5n^3)^7*m^2n")
Simplifying Expressions with Exponents: (m^5n^3)^7 * m^2n
This article will guide you through simplifying the expression (m^5n^3)^7 * m^2n. We'll break down the process step-by-step, using the fundamental rules of exponents.
Understanding the Rules
Before we begin, let's recall some key exponent rules:
- Product of Powers: x^m * x^n = x^(m+n)
- Power of a Power: (x^m)^n = x^(m*n)
- Power of a Product: (x*y)^n = x^n * y^n
Simplifying the Expression
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Apply the Power of a Power Rule: (m^5n^3)^7 = m^(57) * n^(37) = m^35 * n^21
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Apply the Product of Powers Rule: m^35 * n^21 * m^2n = m^(35+2) * n^(21+1) = m^37 * n^22
Final Result
Therefore, the simplified expression is m^37 * n^22.
Key Takeaways
- By applying the rules of exponents, we can efficiently simplify expressions involving powers.
- Understanding these rules allows for a deeper understanding of mathematical relationships.
- Remember to always focus on the individual components and apply the rules systematically.