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a: \(=-25\cdot4-27=-100-27=-127\)
b: \(=-65:\left(-13\right)-25\cdot4=5-100=-95\)
c: \(=100\cdot\left(-47\right)+53\cdot\left(-100\right)=100\cdot\left(-100\right)=-10000\)
d: \(=\left[\left(-3\right)^{13}:3^{10}-73\right]:\left(-5\right)^2-14\)
\(=\left(-100\right):25-14=-4-14=-18\)
7: =6-7+4-3=0
8: =8x5-9x4+4x6=40-36+24=28
3: =231+26-209-26=22
a) $125^3:25^4=(5^3)^3:(5^2)^4=5^9:5^8=5^1$
$16^4:4^2=(4^2)^4:4^2=4^8:4^2=4^6$
$27^8:9^4=(3^3)^8:(3^2)^4=3^{24}:3^8=3^{16}$
$125^5:25^3=(5^3)^5:(5^2)^3=5^{15}:5^6=5^9$
$4^{14}:5^{28}=(2^2)^{14}:5^{28}=2^{28}:5^{28}=(\dfrac{2}{5})^{28}$
b) $12^n:2^{2n}=12^n:(2^2)^n=12^n:4^n=3^n$
$64^4.16^5.4^{20}=(4^3)^4.(4^2)^5.4^{20}=4^{12}.4^{10}.4^{20}=4^{42}$
\(a)\)\(47-\left[\left(45.2^4-5^2.12\right)\div14\right]\)
\(=\)\(47-\left[\left(45.16-25.12\right)\div14\right]\)
\(=\)\(47-\left[\left(720-300\right)\div14\right]\)
\(=\)\(47-\left[420\div14\right]\)
\(=\)\(47-30\)
\(=\)\(17\)
\(b)\)\(10-\left[\left(8^2-48\right).5+\left(2^3.10+8\right)\right]\div28\)
\(=\)\(10-\left[\left(64-48\right).5+\left(8.10+8\right)\right]\div28\)
\(=\)\(10-\left[16.5+\left(80+8\right)\right]\div28\)
\(=\)\(10-\left[16.5+88\right]\div28\)
\(=\)\(10-\left[80+88\right]\div28\)
\(=\)\(10-168\div28\)
\(=\)\(10-6\)
\(=\)\(4\)
c) \(2345-1000:\left[19-2\left(21-18\right)^2\right]\)
= \(2345-1000:\left[19-2.3^2\right]\)
= \(2345-1000:\left[19-2.9\right]\)
= \(2345-1000:\left[19-18\right]\)
= \(2345-1000:1\)
= \(1345\)
a. (9^16.9^14):9^28
=9^16+14:9^28
=9^30-28
=9^2
=81
a) \(\left(9^{16}.9^{14}\right):9^{28}=\left(9^{16+14}\right):9^{28}=9^{30}:9^{28}=9^{30-28}=9^2\)
b) \(\left(5^{32}.5^{19}\right):\left(5^{48}.25\right)=\left(5^{32+19}\right):\left(5^{48}.5^2\right)=5^{51}:\left(5^{48+2}\right)=5^{51}:5^{50}=5^{51-50}=5\)