Question

Scrieti din forma unei singure puteri cu exponent numar natural:

a) 25 la puterea a zecea *5 la puterea 32 *125 la puterea a cincea

b) 9 la puterea a patra * 27 la puterea a cincea * 3 la puterea a paispezecea

c) 2 la puterea a cinsprezecea * 4 la puterea a doisprezecea * 8 la puterea a şasea



P.S: *=ori

Answer 1

$a) {25}^{10} \times {5}^{32} \times {125}^{5}$

$= { {(5}^{2}) }^{10} \times {5}^{32} \times { ({5}^{3} )}^{5}$

$= {5}^{2 \times 10} \times {5}^{32} \times {5}^{3 \times 5}$

$= {5}^{20} \times {5}^{32} \times {5}^{15}$

$= {5}^{20 + 32 + 15}$

$= {5}^{67}$

$b) {9}^{4} \times {27}^{5} \times {3}^{14}$

$= { ({3}^{2} )}^{4} \times {( {3}^{3} )}^{5} \times {3}^{14}$

$= {3}^{2 \times 4} \times {3}^{3 \times 5} \times {3}^{14}$

$= {3}^{8} \times {3}^{15} \times {3}^{14}$

$= {3}^{8 + 15 + 14}$

$= {3}^{37}$

$c) {2}^{15} \times {4}^{12} \times {8}^{6}$

$= {2}^{15} \times { ({2}^{2}) }^{12} \times { ({2}^{3}) }^{6}$

$= {2}^{15} \times {2}^{2 \times 12} \times {2}^{3 \times 6}$

$= {2}^{15} \times {2}^{24} \times {2}^{18}$

$= {2}^{15 + 24 + 18}$

$= {2}^{57}$