Question

Calculati:
(-5) la patrat3 la puterea 4
0 la 2013
(-4) la puterea 3
10 la puterea -2
(2 pe 3) la puterea 3
(1 pe 3) la puterea -2
(radical din 5 pe 10) la patrat
( radical din 5 pe 5)la puterea -2
(- radical din 7 )la puterea 2
(-2 pe radical din 2)totu la patrat

Answer 1

$(-5)^2=(-5)(-5)=25$

$3^4=3\cdot3\cdot3\cdot3 = 81$

$0^{2013} = 0$

$(-4)^3=-64$

$10^{-2} \ = \ \left(\dfrac{1}{10}\right)^2 =\dfrac{1^2}{10^2} = \dfrac{1}{100}$

$\left(\dfrac{2}{3}\right)^3 = \dfrac{2^3}{3^3} = \dfrac{8}{27}$

$\left(\dfrac{1}{3}\right)^{-2} =\left [\left(\dfrac{1}{3}\right)^{-1}\right]^2= \left(\dfrac{3}{1}\right)^2 = \dfrac{9}{1} = 9$

$\left(\dfrac{\sqrt5}{10}\right)^2 = \dfrac{(\sqrt5)^2}{10^2} = {\dfrac{5}{100}}^{(5} = \dfrac{1}{20}$

$(-\sqrt7)^2 = (-\sqrt7)(-\sqrt7) = +\sqrt7\cdot \sqrt7 = 7$

$\left(\dfrac{-2}{\sqrt2}\right)^2 = \dfrac{(-2)^2}{(\sqrt2)^2} = \dfrac{4}{2} = 2$

$\left(\dfrac{\sqrt5}{5}\right)^{-2} = \left[\left(\dfrac{\sqrt5}{5}\right)^{-1}\right]^2 = \left(\dfrac{5}{\sqrt5}\right)^2 = \dfrac{5^2}{(\sqrt5)^2} = \dfrac{25}{5} = 5$