44.
a) \(100-7\left(x-5\right)=58\)
\(\Rightarrow7\left(x-5\right)=100-58\)
\(\Rightarrow7\left(x-5\right)=42\)
\(\Rightarrow x-5=6\)
\(\Rightarrow x=6+5\)
\(\Rightarrow x=11\)
b) \(12\left(x-1\right):3=4^3+2^3\)
\(\Rightarrow4\left(x-1\right)=64+8\)
\(\Rightarrow4\left(x-1\right)=72\)
\(\Rightarrow x-1=\dfrac{72}{4}\)
\(\Rightarrow x-1=18\)
\(\Rightarrow x=18+1\)
\(\Rightarrow x=19\)
c) \(24+5x=7^5:7^3\)
\(\Rightarrow24+5x=7^{5-3}\)
\(\Rightarrow24+5x=7^2\)
\(\Rightarrow5x=49-24\)
\(\Rightarrow5x=25\)
\(\Rightarrow x=\dfrac{25}{5}\)
\(\Rightarrow x=5\)
d) \(5x-206=2^4\cdot4\)
\(\Rightarrow5x-206=16\cdot4\)
\(\Rightarrow5x-206=64\)
\(\Rightarrow5x=206+64\)
\(\Rightarrow5x=270\)
\(\Rightarrow x=\dfrac{270}{5}\)
\(\Rightarrow x=54\)
a) \(4\cdot5^2-81:3^2\)
\(=2^2\cdot5^2-3^4:3^2\)
\(=10^2-3^2\)
\(=100-9\)
\(=91\)
b) \(3^2\cdot22-3^2\cdot19\)
\(=3^2\cdot\left(22-19\right)\)
\(=3^2\cdot3\)
\(=3^3\)
\(=27\)
c) \(2^4\cdot5-\left[131-\left(13-4\right)^2\right]\)
\(=16\cdot5-\left(131-9^2\right)\)
\(=80-\left(131-81\right)\)
\(=80-50\)
\(=30\)
d) \(100:\left\{250:\left[450-\left(4\cdot5^3-2^2\cdot25\right)\right]\right\}\)
\(=100:\left\{250:\left[450-\left(4\cdot125-100\right)\right]\right\}\)
\(=100:\left\{250:\left[450-4\cdot\left(125-25\right)\right]\right\}\)
\(=100:\left[250:\left(450-400\right)\right]\)
\(=100:\left(250:50\right)\)
\(=100:5\)
\(=20\)
43 .
a. 4.52 – 81: 32 = 4.25 – 81:9 = 100 – 9 = 91
43.
b, 3^2. 22 - 3^3.19
= 32.(22-19)
= 32. 3 = 33 =27
b). 2^4.5-[131-(13-4)^2]
=2^4.5-[131-9^2]
=2^4.5-[131-81]
=16.5-50
=80-50
=30
c,100:{250:[450-(4.53-22.25)]}
= 100:{250:[450-(4.125-4.25)]}
= 100:{250:[450-(500-100)]}
= 100:{250:[450-400]}
= 100:{250:50}
= 100:5=20
