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Find the value of 55−6÷555×55−855^{-6} \div 55^{5} \times 55^{-8}55−6÷555×55−8.​
Question

Find the value of 556÷555×55855^{-6} \div 55^{5} \times 55^{-8}.​

A.

552055^{-20}​​

B.

551755^{-17}​​

C.

551355^{-13}​​

D.

551955^{-19}​​

Correct option is D

Given:556÷555×558Formula Used:am÷an=amnam×an=am+nSolution:556÷555×558=5565×558=5511×558=55118=5519Simplified Result:5519or15519\textbf{Given:} \\55^{-6} \div 55^{5} \times 55^{-8} \\\\\textbf{Formula Used:} \\a^m \div a^n = a^{m-n} \\a^m \times a^n = a^{m+n} \\\\\textbf{Solution:} \\55^{-6} \div 55^{5} \times 55^{-8} \\= 55^{-6 - 5} \times 55^{-8} \\= 55^{-11} \times 55^{-8} \\= 55^{-11 - 8} \\= 55^{-19} \\\\\textbf{Simplified Result:} \\\boxed{55^{-19}} \\\text{or} \\\boxed{\dfrac{1}{55^{19}}}​​

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