Math Problem Statement

Simplify \( \frac{x^{-6}}{x^{-2}} \) and write the answer with a positive exponent only.

Solution

The given expression is:

x6x2\frac{x^{-6}}{x^{-2}}

To simplify, use the rule of exponents:

aman=amn\frac{a^m}{a^n} = a^{m-n}

In this case, a=xa = x, m=6m = -6, and n=2n = -2. So,

x6x2=x6(2)=x6+2=x4\frac{x^{-6}}{x^{-2}} = x^{-6 - (-2)} = x^{-6 + 2} = x^{-4}

To express the answer with a positive exponent, we rewrite x4x^{-4} as:

1x4\frac{1}{x^4}

Thus, the simplified expression is:

1x4\frac{1}{x^4}

Would you like further details or have any questions?

Here are some related questions to practice:

  1. Simplify: y3y5\frac{y^{-3}}{y^{-5}}
  2. Simplify: z8z3\frac{z^{-8}}{z^{-3}}
  3. Simplify: a5a2\frac{a^5}{a^2}
  4. Simplify: b0b4\frac{b^0}{b^{-4}}
  5. Simplify: w7w2\frac{w^{-7}}{w^2}

Tip: When simplifying exponents, remember that dividing powers with the same base means subtracting the exponents.

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Math Problem Analysis

Mathematical Concepts

Exponent Rules
Algebra

Formulas

\( \frac{a^m}{a^n} = a^{m-n} \)

Theorems

Exponentiation Rule for Division

Suitable Grade Level

Grades 8-10