Oblicz, stosując własności potęg. Pamiętaj o kolejności wykonywania działań. A) 14^5:28^5(-2)^5. B) 15^3:5^3(1/6)^3 c) (-2/5)^42,5^4:0,5^4 d) (1 1/2)^51,5:0,75^6 e) (3 1/3)^14:(3 1/3)^4(-3/10)^10 f) 3^23^3:3^4. G) 4^4:2^3:2^2 h) (3 1/3)^2:(1 3/9)^2. I) 1/(1 2/3)^4:(3/5)^6
.

[tex]15^3:5^3\cdot\left(\dfrac{1}{6}\right)^3=\left(15:5\cdot\left(\dfrac{1}{6}\right)\right)^3=\left(3\cdot\left(\dfrac{1}{6}\right)\right)^3=\left(\dfrac{1}{2}\right)^3=\dfrac{1}{8}[/tex]

c)

[tex]\left(-\dfrac{2}{5}\right)^4\cdot2,5^4:0,5^4=\left(-\dfrac{2}{5}\cdot\dfrac{5}{2}:\dfrac{1}{2}\right)^4=\left(-1\cdot\dfrac{2}{1}\right)^4=(-2)^4=16[/tex]

d)

[tex]\left(1\dfrac{1}{2}\right)^5\cdot1,5:0,75^6=\left(\dfrac{3}{2}\right)^5\cdot\dfrac{3}{2}:\left(\dfrac{3}{4}\right)^6=\left(\dfrac{3}{2}\right)^6\cdot\left(\dfrac{4}{3}\right)^6=\left(\dfrac{3}{2}\cdot\dfrac{4}{3}\right)^6=2^6=64[/tex]

e)

[tex]\left(3\dfrac{1}{3}\right)^{14}:\left(3\dfrac{1}{3}\right)^4\cdot\left(-\dfrac{3}{10}\right)^{10}=\left(3\dfrac{1}{3}\right)^{10}\cdot\left(-\dfrac{3}{10}\right)^{10}=\left(\dfrac{10}{3}\cdot\left(-\dfrac{3}{10}\right)\right)^{10}=\\=\left(-1\right)^{10}=1[/tex]

f)

[tex]3^2\cdot3^3:3^4=3^5:3^4=3[/tex]

g)

[tex]4^4:2^3:2^2=(2^2)^4:2^3:2^2=2^8:2^3:2^2=2^5:2^2=2^3=8[/tex]

h)

[tex]\left(3\dfrac{1}{3}\right)^2:\left(1\dfrac{3}{9}\right)^2=\left(\dfrac{10}{3}:\dfrac{12}{9}\right)^2=\left(\dfrac{10}{3}\cdot\dfrac{3}{4}\right)^2=\left(\dfrac{5}{2}\right)^2=\dfrac{25}{4}=6\dfrac{1}{4}[/tex]

i)

[tex]\dfrac{1}{\left(1\dfrac{2}{3}\right)^4}:\left(\dfrac{3}{5}\right)^6=\left(\dfrac{5}{3}\right)^{-4}:\left(\dfrac{3}{5}\right)^6=\left(\dfrac{5}{3}\right)^{-4}\cdot\left(\dfrac{5}{3}\right)^6=\left(\dfrac{5}{3}\right)^2=\dfrac{25}{9}=2\dfrac{7}{9}[/tex]