Poziom A:
[tex]a)\ \ 2\cdot2^2\cdot2^5=\big2^{1+2+5}=2^8\\\\b)\ \ 5^8:5^6=\big5^{8-6}=5^2\\\\c)\ \left(\dfrac13\right)^4\cdot\left(\dfrac13\right)^2\cdot\left(\dfrac13\right)^0= \left(\dfrac13\right)^{4+2+0}=\left(\dfrac13\right)^6\\\\ d)\ \left(-\dfrac12\right)^2\cdot\left(-\dfrac12\right)^2=\left(-\dfrac12\right)^{2+2}=\left(-\dfrac12\right)^4[/tex]
Poziom B:
[tex]a)\ \ 3^7:3^2\cdot3^5=\big3^{7-2+5}=3^{10}\\\\b)\ \ 0,2^4\cdot0,2^3:0,2^2= \big2^{4+3-2}=2^5\\\\c)\ \left(-\dfrac14\right)^5\cdot\left(-\dfrac14\right)^4:\left(-\dfrac14\right)^2=\left(-\dfrac14\right)^{5+4-2}=\left(-\dfrac14\right)^7[/tex]
Korzystamy z własności potęg o tych samych podstawach:
[tex]\big a^{\,x}\cdot\big a^{\,y}=\big a^{\,x+ y}\\\\ \big a^{\,x}:\big a^{\,y}= \big a^{\,x- y}[/tex]
