[tex](2¹⁰ \times 3⁷)⁹ : (2⁵ \times 3⁶)¹⁰= \\ ( {2}^{10 \times 9} \times {3}^{7 \times 9} ) : ( {2}^{5 \times 10} \times {3}^{6 \times 10} )= \\ ( {2}^{90} \times {3}^{63} ) : ( {2}^{50} \times {3}^{60} )= \\ {2}^{90 - 50} \times {3}^{63 - 60} = \\ {2}^{40} \times {3}^{3} [/tex]
[tex] {2}^{47} \div {2}^{39} = {2}^{47 - 39} = {2}^{8} [/tex]
[tex] {( {2}^{17}) }^{8} \times {2}^{31} = \\ {2}^{17 \times 8} \times {2}^{31} = \\ {2}^{136} \times {2}^{31} = \\ {2}^{136 + 31} = \\ = {2}^{167} [/tex]
