Question

[Le Thu Trang]

( ( \(^{3^2}\)) ) \(^{^2}\) - ( ( -\(^{5^2}\)) )\(^{^2}\) + ( ( -\(^{2^3}\)) )\(^{^2}\)

\(^{2^4}\)+ 8[(-2)\(^{^2}\) : \(\dfrac{1}{2}\) ]\(^{^0}\) - 2\(^{^{-2}}\) . 4 + (-2)\(^{^2}\)

\(^{2^4}\)+ 3(\(\dfrac{1}{2}\))\(^{^0}\) + 2\(^{^{-2}}\) . 8 + [(-2)\(^{^3}\) . \(\dfrac{1}{2^4}\) ] . 2 - \(\dfrac{1}{2}\)

\(\dfrac{15^{10}.5^{10}}{75^{10}}\) + \(\dfrac{\left(0,8\right)^5}{\left(0,4\right)^6}\)

\(\dfrac{2^{13}.9^4}{6^3.8^3}\)

Answer 1

[Son Hak]

((3\(^2\)))\(^2\) - ((-5\(^2\)))\(^2\) + ((-2\(^3\)))\(^2\)

= 81 - 625 + 64

= -544+ 64

= -480

2\(^4\) + 8[(-2)\(^2\) :\(\dfrac{1}{2}\)]\(^0\) - 2\(^{-2}\). 4 + (-2)\(^2\)

= 16+ 8.1 - \(\dfrac{1}{4}\). 4 + 4

= 16+ 8- 1+4

= 27

2\(^4\) + 3(\(\dfrac{1}{2}\))\(^0\) + 2\(^{-2}\).8 + [(-2)\(^3\). \(\dfrac{1}{2^4}\)].2 - \(\dfrac{1}{2}\)

= 16 + 3.1 +\(\dfrac{1}{4}\).8 + [(-8).\(\dfrac{1}{16}\)].2 -\(\dfrac{1}{2}\)

= 16 + 3+ 2 + \(\dfrac{-1}{2}\).2- \(\dfrac{1}{2}\)

= 21 + (-1)- \(\dfrac{1}{2}\)

= 20-\(\dfrac{1}{2}\) = \(\dfrac{40}{2}\) - \(\dfrac{1}{2}\)= \(\dfrac{39}{2}\)

\(\dfrac{15^{10}.5^{10}}{75^{10}}\) + \(\dfrac{\left(0,8\right)^5}{\left(0,4\right)^6}\)

= \(\dfrac{\left(15.5\right)^{10}}{75^{10}}\) + \(\dfrac{\left(0,4.2\right)^5}{\left(0.4\right)^6}\)

= \(\dfrac{75^{10}}{75^{10}}\) + \(\dfrac{\left(0,4\right)^5.2^5}{\left(0,4\right)^6}\)

= 1 + \(\dfrac{2^5}{0,4}\) = 1+ 80 = 81

\(\dfrac{2^{13}.9^4}{6^3.8^3}\)

= \(\dfrac{2^{13}.\left(3^2\right)^4}{\left(2.3\right)^3.\left(2^3\right)^3}\) = \(\dfrac{2^{13}.3^8}{2^3.3^3.2^9}\)

= \(\dfrac{2^4.3^5}{2^3}\) = 2.3\(^5\) = 486