Question

d) (7 la puterea 2 + 7 la.puterea 3 + 7 la puterea 4): 7 la puterea 2;
e) (2 la puterea 2010 + 2 la puterea 2011 + 2 la puterea 2012 + 2 la puterea 2013 + 2 la puterea 2014) : 2 la puterea 2008
f) (3 la puterea 195 + 3 la puterea 197) : (3 la puterea 64) la puterea 3
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Answer 1

Explicație pas cu pas:

$d) \: \: ( {7}^{2} + {7}^{3} + {7}^{4} ) \div {7}^{2} = ( {7}^{2} + {7}^{2} \times 7 + {7}^{2} \times {7}^{2} ) \div {7}^{2} = {7}^{2} \times (1 + 7 + {7}^{2} ) \div {7}^{2} = 1 + 7 + 49 = 57$

$e) \: \: ( {2}^{2010} + {2}^{2011} + {2}^{2012} + {2}^{2013} + {2}^{2014} ) \div {2}^{2008} = {2}^{2008} \times ( {2}^{2} + {2}^{3} + {2}^{4} + {2}^{5} + {2}^{6} ) \div {2}^{2008} = 4 + 8 + 16 + 32 + 64 = 124$

$f) \: \: ( {3}^{195} + {3}^{197} ) \div ( {3}^{64})^{3} = ( {3}^{195} + {3}^{197} ) \div {3}^{192} = {3}^{192} \times ( {3}^{3} + {3}^{5} ) \div {3}^{192} = 27 + 243 = 270$