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Find the value of 40−7÷(4019×404)40^{-7} ÷ (40^{19}× 40^4)40−7÷(4019×404)
Question

Find the value of 407÷(4019×404)40^{-7} ÷ (40^{19}× 40^4)

A.

-33

B.

-29

C.

-30

D.

-28

Correct option is C

Given:
407÷(4019×404)40^{-7} \div (40^{19} \times 40^{4}) \\ 
Formula Used:
am÷an=amnam×an=am+na^m \div a^n = a^{m-n} \\a^m \times a^n = a^{m+n} \\ 
Solution:
407÷(4019×404)=>407÷40(19+4)=>407÷4023=>40723=4030407÷(4019×404)=403040^{-7} \div (40^{19} \times 40^4) \\\Rightarrow 40^{-7} \div 40^{(19+4)} \\\Rightarrow 40^{-7} \div 40^{23} \\\Rightarrow 40^{-7 - 23} = 40^{-30} \\\therefore 40^{-7} \div (40^{19} \times 40^4) = 40^{-30}​​

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