Question

por favor alguien que me ayude con estos ejercicios de potenciacion....

Answer 1

Respuesta:

EJERCICIO 19

$(\frac{k^{3t+2} }{k^{2+3t} }) ^{10} =\frac{k^{30t+20} }{k^{20+30t} }=k^{30t+20-(20+30t)}=k^{0} =1$

EJERCICIO 20

$(\frac{a^{3m-1}*a^{2m-2} }{a^{4m-3} }) ^{8} =(\frac{a^{24m-8}*a^{16m-16} }{a^{32m-24} }) } =(\frac{a^{24m-8+16m-16} }{a^{32m-24} }) =(\frac{a^{40m-24} }{a^{32m-24} }) =\\\\a^{40m-24-(32m-24)} =a^{8m}$

EJERCICIO 21

$(\frac{x^{2a-b}*x^{b+2a} }{x^{2a} *x^{3b} }) ^{4a+3b} = \frac{x^{8a^{2}+2ab-3b^{2}}*x^{8a^{2}+10ab+3b^{2}}}{x^{8a^{2}+6ab}*x^{6ab+9b^{2} } } =\\\\\\\frac{x^{{8a^{2}+2ab-3b^{2}}+8a^{2}+10ab+3b^{2} }}{x^{8a^{2}+6ab+6ab+9b^{2}} }=\frac{x^{16a^{2}+12ab } }{x^{8a^{2}+12ab+9b^{2} } } =\\\\x^{16a^{2}+12ab- (8a^{2}+12ab+9b^{2})} =x^{8a^{2}+9b^{2} }$

EJERCICIO 22

$(\frac{n^{5x} }{n^{3x+1} } *\frac{n^{2x} }{n^{3} } )^{x-2} =\frac{n^{5x^{2} -10x} }{n^{3x^{2} -5x-2} } *\frac{n^{2x^{2} -4x} }{n^{3x-6} }\\\\\frac{n^{5x^{2} -10x+2x^{2} -4x}}{n^{3x^{2} -5x-2+3x-6} } =n^{5x^{2} -10x+2x^{2} -4x-(3x^{2} -5x-2+3x-6)} \\\\n^{4x^{2}-12x+8 }$

EJERCICIO 23

$(\frac{64^{2x-3} }{128^{x-1} }) ^{5x+11}= (\frac{(2^{6}) ^{2x-3} }{(2^{7} )^{x-1} }) ^{5x+11}\\\\(\frac{2^{12x-18} }{2^{7x-7} }) ^{5x+11} = ({2^{12x-18-(7x-7)} }}) ^{5x+11} \\\\({2^{5x-11} }}) ^{5x+11} =2^{25x^{2} -121}$