%5E2%2F2m%5E5n.jpeg "(4m^2n)^2/2m^5n")
Simplifying Algebraic Expressions: (4m^2n)^2 / 2m^5n
This article will guide you through simplifying the algebraic expression (4m^2n)^2 / 2m^5n. Let's break down the process step-by-step.
Understanding the Expression
The expression involves:
- Exponents: We have (4m^2n)^2, which means we need to square the entire term within the parentheses.
- Division: The expression involves dividing the squared term by 2m^5n.
Simplifying the Expression
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Square the term in parentheses:
(4m^2n)^2 = 4^2 * (m^2)^2 * n^2 = 16m^4n^2
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Rewrite the expression:
Now we have: 16m^4n^2 / 2m^5n
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Simplify by dividing coefficients and subtracting exponents:
- Coefficients: 16 / 2 = 8
- m exponents: m^4 / m^5 = m^(4-5) = m^-1
- n exponents: n^2 / n = n^(2-1) = n^1
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Combining terms:
This gives us: 8 * m^-1 * n^1 = 8n/m
Final Answer
Therefore, the simplified form of (4m^2n)^2 / 2m^5n is 8n/m.
Key Points to Remember
- Exponent rules: When raising a term to a power, we apply the power to each factor within the term.
- Division of exponents: When dividing terms with the same base, we subtract the exponents.
- Negative exponents: A negative exponent indicates a reciprocal. For example, m^-1 = 1/m.
By applying these rules, we successfully simplified the given algebraic expression.