Math Problem Statement

Wrote without a fraction: (a^(-n))/(a^(2+n))

Solution

To write the expression ana2+n\frac{a^{-n}}{a^{2+n}} without a fraction, you can use the properties of exponents. Specifically, you can subtract the exponent of the denominator from the exponent of the numerator:

ana2+n=an(2+n)\frac{a^{-n}}{a^{2+n}} = a^{-n - (2+n)}

Simplify the exponent:

an2n=a2n2a^{-n - 2 - n} = a^{-2n - 2}

So, the expression ana2+n\frac{a^{-n}}{a^{2+n}} simplifies to:

a2n2a^{-2n - 2}

Would you like further details on how to simplify similar expressions, or do you have any questions?

Here are 5 related questions:

  1. How do you simplify aman\frac{a^m}{a^n} when mm and nn are different?
  2. What is the simplified form of a2a4\frac{a^{-2}}{a^4}?
  3. How do you express a3na2n\frac{a^{3-n}}{a^{2n}} without using a fraction?
  4. How do you simplify the expression axay\frac{a^{-x}}{a^{-y}}?
  5. What is the result of multiplying two powers of the same base, am×ana^m \times a^n?

Tip: When dividing powers with the same base, subtract the exponents to simplify the expression.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponentiation

Formulas

a^m / a^n = a^(m-n)
Negative exponent rule: a^(-n) = 1/(a^n)

Theorems

Laws of Exponents

Suitable Grade Level

Grades 9-10