Math Problem Statement

Simplify

Simplify the given expression involving exponents.

Solution

The simplified form of the given expression is:

132ab8\frac{1}{32ab^8}

Would you like further details on the steps involved? Here are five related questions to expand your understanding:

  1. How are negative exponents handled when simplifying expressions?
  2. What rules of exponents were used in this simplification?
  3. How does distributing exponents across fractions work?
  4. How would the expression change if the exponents were positive initially?
  5. Can you express the simplified form in decimal notation?

Tip: Always simplify inside parentheses first before applying exponent rules to the whole expression.

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Math Problem Analysis

Mathematical Concepts

Exponentiation
Simplification
Algebraic Fractions

Formulas

Negative Exponent Rule: a^(-n) = 1 / a^n
Power of a Quotient Rule: (a/b)^n = (a^n) / (b^n)
Power of a Power Rule: (a^m)^n = a^(m * n)

Theorems

Laws of Exponents
Properties of Fractions

Suitable Grade Level

Grades 10-12