Question

Scrieți sub formă de puteri cu aceeași bază

$a) {2}^{16} si {8}^{4}$
$b) {81}^{5} si \: {27}^{3}$
$c) {125}^{3} si \: {25}^{6}$

$d)( \frac{8}{27} {)}^{3} \: si( \frac{4}{9} {)}^{5}$
$c)( \frac{125}{27} {)}^{3} si( \frac{5}{3} {)}^{4}$
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Answer 1

Răspuns:

$a)\\2^{16} \\8^{4} = 2^{3^{4} } = 2^{12} \\\\b)\\81^{5} = 3^{3^{5} } = 3^{15}\\ 27^{3} = 3^{9} \\\\c)\\125^{3} = 5^{3^{3} } = 5^{9} \\25^{6} = 5^{2^{6} } = 5^{12} \\\\d)\\\frac{8}{27}^{3} = \frac{2^{3} }{3^{3} }^{3} = (\frac{2}{3})^{9}\\\frac{4}{9}^{5} = \frac{2}{3}^{10} \\\\e)\\\frac{125}{27}^{3} = \frac{5}{3}^{9} \\\frac{5}{3}^{4}$