Which of the following results in $- 9$ ?

3^{6} \div 3^{4}

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- (3)^{6} \div (3)^{4}

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(- 3)^{6} \div (- 3)^{4}

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(- 3)^{4} \div (- 3)^{6}

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Solution

The correct option is B $- (3)^{6} \div (3)^{4}$
Option A: $(3)^{6} \div (3)^{4} = [\frac{3^{6}}{3^{4}}] = [3^{6 - 4}] = 3^{2} = 9$

Option B: $- (3)^{6} \div (3)^{4} = - [\frac{3^{6}}{3^{4}}] = - [3^{6 - 4}] = - 3^{2} = - 9$

Option C: $(- 3)^{6} \div (- 3)^{4} = [\frac{3^{6}}{3^{4}}] = [3^{6 - 4}] = 3^{2} = 9$

Option D: $(- 3)^{4} \div (- 3)^{6} = [\frac{3^{4}}{3^{6}}] = [3^{4 - 6}] = 3^{- 2} = \frac{1}{9}$

So, option $B$ is correct.

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