[tex]a)\\{}\quad \ 2^9\cdot5^7=2^{2+7}\cdot5^7=2^2\cdot2^7\cdot5^7= 4\cdot(2\cdot5)^7=4\cdot10^7=40\,000\,000\\\\b)\\{}\quad\ 0,2^6\cdot5^3=0,2^{3+3}\cdot5^3=0,2^3\cdot0,2^3\cdot5^3=0,008\cdot(0,2\cdot5)^3=\\\\{}\qquad \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad \qquad= 0,008\cdot1^3=0,008[/tex]
[tex]c)\\{}\quad\ \left(\dfrac23\right)^6:\left(\dfrac49\right)^5= \left(\dfrac23\right)^{1+5}\cdot\left(\dfrac94\right)^5= \left(\dfrac23\right)^1\cdot\left(\dfrac23\right)^5\cdot\left(\dfrac94\right)^5=\\\\ {}\quad\ \ =\dfrac23\cdot\left(\dfrac23\cdot\dfrac94\right)^5= \dfrac23\cdot\left(\dfrac32\right)^5=\dfrac23\cdot\dfrac{243}{32}\,=\,\dfrac{81}{16}\,=\,5\dfrac1{16}[/tex]
