Simplify the expression. Express final results without using zero or negative integers as exponents. ( a b ² c ^{- 1} ) ^{- 5} A) $\frac { c ^ { 5 } } { a ^ { 5 } b ^ { 10 } }$ B) $\frac { a ^ { 5 } b ^ { 10 } } { c ^ { 5 } }$ C) $a ^ { 5 } b ^ { 10 } c ^ { 5 }$

Question

Quizplus · Accepted Answer

- Simplify the expression within the parentheses first: 
    - $\text{( }a \text{ } b^2 \text{ } c^{-1} \text{ )}^5$ = $a^5 \text{ } b^{10} \text{ } c^{-5}$ 
- Then simplify the entire expression: 
    - $a^5 \text{ } b^{10} \text{ } c^{-5} \text{ } c^5$ = $a^5 \text{ } b^{10} \text{ } \frac{c^5}{c^5}$ = $a^5 \text{ } b^{10}$ / $c^0$ = $a^5 \text{ } b^{10} \text{ } / \text{ } 1$ = $\frac{a^5 \text{ } b^{10}}{1}$ = $a^5\text{ } b^{10}$ / $c^0$ = $\frac{c^5}{a^5 \text{ } b^{10}}$ $$ \because \frac{1}{x^0} = 1 \text{ and } c^{-5} = \frac{1}{c^5}$$ 
- Since the question asks for final results without using zero or negative integers as exponents, we cannot have $c^0$ in the answer. Therefore, option A is the best choice.

Simplify the Expression c5a5b10\frac { c ^ { 5 } } { a ^ { 5 } b ^ { 10 } }a5b10c5​

Simplify the Expression $\frac { c ^ { 5 } } { a ^ { 5 } b ^ { 10 } }$