Question

Aratati ca urmatoarele numere sunt patrate perfecte:a)25 la puterea 37,b)to a puterea 75,c)625 la puterea 7,d )9 la puterea 27,e)121 la puterea 121, f) (2×8)17
g)32 la puterea 19 : 2la puterea 19,h)81 la puterea 125.
Va rog ajutati.ma!Niciodata nu le.am inteles!

Answer 1

$\bf a) \: 25^{37} = \big(5^{2} \big )^{37} = \blue{\big(5^{37} \big )^{2}\rightarrow patrat \: perfect}$

$\bf b) \: 4^{75} = \big(2^{2} \big )^{75} = \green{\big(2^{75} \big )^{2}\rightarrow patrat \: perfect}$

$\bf c) \: 625^{7} = \big(25^{2} \big )^{7} = \orange{\big(25^{7} \big )^{2}\rightarrow patrat \: perfect}$

$\bf d) \: 9^{27} = \big(3^{2} \big )^{27} = \red{\big(3^{27} \big )^{2}\rightarrow patrat \: perfect}$

$\bf e) \: 121^{121} = \big(11^{2} \big )^{121} = \purple{\big(11^{121} \big )^{2}\rightarrow patrat \: perfect}$

$\bf f) \: \big(2 \cdot8 \big)^{17} = \big(4^{2} \big )^{17} = \pink{\big(4^{17} \big )^{2}\rightarrow patrat \: perfect}$

$\bf g) \: 32^{19}:2^{19} =\big(2^{5} \big )^{19} :2^{19}=2^{5\cdot19} :2^{19}=$

$\bf 2^{95 - 19} = 2^{76} = \blue {\big(2^{23} \big )^{2}\rightarrow patrat \: perfect}$

$\bf h) \: 81^{125} = \big(9^{2} \big )^{125} = \green{\big(9^{125} \big )^{2}\rightarrow patrat \: perfect}$