Explicație pas cu pas:
a.
[tex] {4}^{16} = ({ {2}^{2} })^{16} = {2}^{2 \times 16} = {2}^{32} \\ {8}^{12} = ({ {2}^{3} })^{12} = {2}^{3 \times 12} = {2}^{36} \\ {16}^{15} = ({ {2}^{4} })^{15} = {2}^{4 \times 15} = {2}^{60} [/tex]
[tex] {4}^{16} \times {8}^{12} \times {16}^{15} = {2}^{32} \times {2}^{36} \times {2}^{60} \\ = {2}^{32 + 36 + 60} = {2}^{128} [/tex]
[tex] b )\: {25}^{10} = ( { {5}^{2} })^{10} = {5}^{2 \times 10} = {5}^{20} \\ {125}^{5} =( {5}^{3} )^{5} = {5}^{3 \times 5} = {5}^{15} \\ {25}^{10} \times {5}^{23} \times {125}^{5} = {5}^{20} \times {5}^{23} \times {5}^{15} = \\ {5}^{20 + 23 + 15} = {5}^{58} [/tex]
[tex]c) \: {9}^{4} = ( { {3}^{2} })^{4} = {3}^{2 \times 4} = {3}^{8} \\ {27}^{5} = ( { {3}^{3} })^{5} = {3}^{3 \times 5} = {3}^{15} \\ {9}^{4} \times {27}^{5} \times {3}^{14} = {3}^{8} \times {3}^{15} \times {3}^{14} = \\ {3}^{8 + 15 + 14} = {3}^{37} [/tex]
