Question

Puteti sa ma ajutati?

Answer 1

$\displaystyle 3a).5 ^{8 ^{2} } :25 ^{2 ^{5} } =5^{64}:25^{32}=6^{64}:(5^2)^{32}=5^{64}:5^{64}=5^{64-64}=5^0=1 \\ b).3^{42}:\left(3^{35}\cdot 3^4\right) \cdot \left(3^3+3 \cdot 11\right):15=3^{42}:3^{35+4}\cdot \left(27+33\right):15= \\ =3^{42}:3^{39}\cdot 60:15=3^{42-39}\cdot 4=3^3 \cdot 4=27 \cdot 4=108$
$\displaystyle c).12^2+\left[2 ^{4 ^{3} } :\left(2^9\right)^7+5^{60}: \left(5 \cdot 5^3 \right)^{15}\right]= \\ =144+\left[2^{64}:2^{63}+5^{60}:\left(5^{1+3}\right)^{15}\right]=144+\left[2^{64-63}+5^{60}:\left(5^4\right)^{15}\right]= \\ =144+ \left(2^1+5^{60}:5^{60}\right)=144+\left(2+5^{60-60}\right)=144+\left(2+5^0\right)= \\ =144+(2+1)=144+3=147$
$\displaystyle d).\left[\left(2 \cdot 3 \cdot 5\right)^2-7^5:7^3\right]:8^0-2^4 \cdot 5^2=\left(30^2-7^{5-3}\right):1-16 \cdot 25= \\ = \left(900-7^2\right):1-16 \cdot 25=\left(900-49\right):1-16 \cdot 25= \\ =851:1-16 \cdot 25=851-16 \cdot 25=851-400=451$