Math Problem Statement

Simplify \( \frac{x^{-6}}{x^{-7}} \)

Solution

Let's simplify the given expression:

x6x7\frac{x^{-6}}{x^{-7}}

Step-by-step Solution:

  1. Use the rule of exponents for division: aman=amn.\frac{a^m}{a^n} = a^{m-n}. Apply this rule to the expression: x6(7)=x6+7.x^{-6 - (-7)} = x^{-6 + 7}.

  2. Simplify the exponent: 6+7=1.-6 + 7 = 1.

  3. Therefore, the simplified result is: x1=x.x^1 = x.

Final Answer:

xx

Would you like further explanation or examples? 😊


Here are 5 related questions to deepen understanding:

  1. How do you simplify x3x5\frac{x^3}{x^{-5}}?
  2. What happens when you simplify x0x4\frac{x^0}{x^{-4}}?
  3. How would the rule change if the base was yy instead of xx?
  4. Can you explain why x0=1x^0 = 1 in exponent rules?
  5. How do you simplify (x3y4)/(x1y2)(x^{-3}y^{-4}) / (x^{-1}y^{-2})?

Tip: Always remember that when dividing exponents with the same base, subtract the powers (am/an=amna^m / a^n = a^{m-n}).

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Math Problem Analysis

Mathematical Concepts

Exponent Rules
Simplifying Algebraic Expressions

Formulas

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

Theorems

Properties of Exponents

Suitable Grade Level

Grades 8-10