Question

Calculeaza (11²⁰¹¹×4¹⁰⁰⁵)÷[(22²)⁵]²⁰¹=
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Answer 1

Răspuns:

Explicație pas cu pas:

4^1005 = (2^2)^1005 = 2^2010

11^2011 = 11×11^2010

11^2011×4^1005 = 11×11^2010×2^2010 = 11×(11×2)^2010 = 11×22^2010

________

[(22^2)^5]^201 = (22^10)^201 = 22^2010

___________

11*22^2010 : 22^2010 = 11

Answer 2

$(11 {}^{2011} \times 4 {}^{1005} ) : (22 {}^{10} ) {}^{201} \\ \\ = (11 {}^{2011} \times 4 {}^{1005} ) : 22 {}^{2010} \\ \\ = \frac{11 {}^{2011} \times 4 {}^{1005} }{22 {}^{2010} } \\ \\ = \frac{11 {}^{2011} \times \sout{2 {}^{2010}} }{11 {}^{2010} \times\sout{ 2 {}^{2010} } } \\ \\ = \frac{11 {}^{2011} }{ {11}^{2010} } \\ \\ = 11 {}^{2011 - 2010} \\ \\ = 11$