a) \(3^{10}:3^6-2^3.2^2\)
\(=3^{10-6}-2^{3+2}\)
\(=3^4-2^5\)
\(=81-32\)
\(=49\)
b) \(\left(3.4^2.2^7\right)^2:\left(3^2.2^{20}\right)\)
\(=\left(3^2.4^4.2^{14}\right):\left(3^2.2^{20}\right)\)
\(=\left(2^8.2^{14}\right):2^{20}\)
\(=2^{22}:2^{20}\)
\(=2^2\)
\(=4\)
c) \(\left(2^3.9^4+9^3.45\right):\left(9^2.10-9^2\right)\)
\(=\left[9^3.\left(2^3.9+45\right)\right]:\left[9^2.\left(10-1\right)\right]\)
\(=\left(9^3.117\right):9^3\)
\(=117\)
d) \(24^4:3^4-32^{12}:16^{12}\)
\(=8^4-2^{12}\)
\(=\left(2^3\right)^4:2^{12}\)
\(=2^{12}:2^{12}\)
\(=1\)
e) \(\left(2^9.3+2^9.5\right):2^{12}\)
\(=\left[2^9.\left(3+5\right)\right]:2^{12}\)
\(=\left(2^9.2^3\right):2^{12}\)
\(=2^{12}:2^{12}\)
\(=1\)
f) \(\left(2^4.5^2.11^2.7\right):\left(2^3.5^3.7^2.11\right)\)
\(=\left(2.11\right):\left(5.7\right)\)
\(=22:35\)
\(=\dfrac{22}{35}\)
g) \(\left(2^{10}.3^{10}-2^{10}.3^9\right):\left(2^9.3^{10}\right)\)
\(=\left[2^{10}.3^9.\left(3-1\right)\right]:\left(2^9.3^{10}\right)\)
\(=\left(2^{11}.3^9\right):\left(2^9.3^{10}\right)\)
\(=2^2:3\)
\(=\dfrac{4}{3}\)
h) \(\left(11.3^{22}.3^7-9^{15}\right):\left(2.3^{14}\right)^2\)
\(=\left(11.3^{29}-3^{30}\right):\left(2^2.3^{28}\right)\)
\(=\left[3^{29}.\left(11-3\right)\right]:\left(2^2.3^{28}\right)\)
\(=\left(3^{29}.2^3\right):\left(2^2.3^{28}\right)\)
\(=3.2\)
\(=6\)
