Math Problem Statement

(-n)^2(2n)^-1

Solution

Let's simplify the given expression:

(n)2(2n)1(-n)^2(2n)^{-1}

Step 1: Simplify (n)2(-n)^2

Squaring n-n gives:

(n)2=n2(-n)^2 = n^2

Step 2: Simplify (2n)1(2n)^{-1}

The exponent 1-1 means taking the reciprocal, so:

(2n)1=12n(2n)^{-1} = \frac{1}{2n}

Step 3: Combine both parts

Now, combine n2n^2 and 12n\frac{1}{2n}:

n2×12n=n22nn^2 \times \frac{1}{2n} = \frac{n^2}{2n}

Step 4: Simplify the fraction

Cancel one nn from the numerator and denominator:

n22n=n2\frac{n^2}{2n} = \frac{n}{2}

Final Answer:

n2\frac{n}{2}

Would you like more details or have any questions about this process? Here are some related questions:

  1. How would the result change if the exponent on nn was negative instead of positive?
  2. Can you simplify an expression with multiple variables in a similar way?
  3. What happens if the exponent of the term nn is fractional?
  4. How would you solve expressions involving negative exponents and roots?
  5. How do you handle cases where both terms have negative exponents?

Tip: When simplifying expressions with negative exponents, always remember that a negative exponent means the reciprocal of the base raised to the positive exponent.

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Math Problem Analysis

Mathematical Concepts

Exponents
Algebra
Fraction Simplification

Formulas

a^m * a^n = a^(m+n)
(a^m)^n = a^(m*n)
a^(-n) = 1 / a^n

Theorems

Laws of Exponents

Suitable Grade Level

Grades 8-10