Question

repede ofer 10 puncte !!! efectuati f) x=[(2^5+2^5+2^5+...+2^5)de 16 ori :4^4+(3^7+3^7+3^7+...+3^7)de 81 de ori:9^5]^15:25^7

Answer 1

$[\underbrace{(2^5+2^5+...+2^5)}_{16} : 4^4+\underbrace{(3^7+3^7+...+3^7)}_{81} : 9^5]^{15}:25^7= \\\\\\ = [16*2^5:(2^2)^4+81*3^7:(3^2)^5]^{15}:25^7= \\\\=(2^4*2^5:2^8+3^4*3^7:3^{10}]^{15}:25^7= \\\\= (2^9:2^8+3^{11}:3^{10})^{15}:(5^2)^7= \\\\= (2+3)^{15}: 5^{14}= \\\\= 5^{15}:5^{14}= \\\\= \boxed{5}$