Math Problem Statement

Simplify the algebraic expression involving exponents and fractions: \[ \frac{6^4 c^{-5} - 6^3 c^{-4} + b^2 - c^{-3} + b c^{-2}}{3^4 c^{-5} + b c^{-3} + 5b c + 5 c^5} \div \frac{b^4 c^3 - b c^2 c^5}{b^2 c^5} \]

Solution

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Please give me a moment.The expression you uploaded contains several terms with powers of variables bb and cc, as well as some operations (addition, subtraction, and division).

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64c−5−63c−4+b2−c−3+bc−234c−5+bc−3+5bc+5c5÷b4c3−bc2c5b2c5\frac{6^4 c^{-5} - 6^3 c^{-4} + b^2 - c^{-3} + b c^{-2}}{3^4 c^{-5} + b c^{-3} + 5b c + 5 c^5} \div \frac{b^4 c^3 - b c^2 c^5}{b^2 c^5}

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponent Rules
Fraction Operations

Formulas

Exponent Rules: a^m * a^n = a^(m+n), a^m / a^n = a^(m-n)
Fraction Division: (A/B) ÷ (C/D) = (A/B) * (D/C)

Theorems

Laws of Exponents
Fraction Simplification

Suitable Grade Level

Grades 9-12

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