Question

15 la puterea 2 -5 ×[(5 la puterea 7 ) totul la puterea 8 ÷5la puterea 30 +5 ×5la puterea 21-5 la puterea 26 ] ÷ 25la puterea 10

Answer 1

$15^2-5\cdot [(5^7)^8:5^{30}+5\cdot 5^{21}-5^{26}]:25^{10}=\\225-5\cdot [5^{56}:5^{30}+5^{22}-5^{26}]:(5^2)^{10}=\\225-5\cdot (5^{26}+5^{22}-5^{26}):5^{20}=\\225-5\cdot 5^{22}:5^{20}=\\225-5^{23}:5^{20}=\\225-5^3=\\225-125=\boxed{100}\\\text{Am folosit formulele:}\\\bullet (a^m)^n=a^{m\cdot n}\\\bullet a^m\cdot a^n=a^{m+n}\\\bullet a^m:a^n=a^{m-n}$

Answer 2

15^2 - 5 x [(5^7)^8 : 5^30 + 5 x 5^21 - 5^26] : 25^10 =

15^2 - 5 x [5^56 : 5^30 + 5^22 - 5^26 ] : (5^2)^10 =

15^2 - 5 x [ 5^26 + 5^22 - 5^26] ; 5^20 =

15^2 - 5 x 5^22 : 5^20 =

15^2 - 5^(1+22-20) =

15^2 - 5^3 =

225 - 125 =

100