Степен степна

Текст задатака објашњених у видео лекцији:

Пр.1) Упростити следеће изразе:

а) ${\left( {{m^3}} \right)^4} = $

б) ${\left( {{{\left( {{x^4}} \right)}^5}} \right)^6} = $

в) ${\left( {{{\left( { - 3} \right)}^2}} \right)^7} = $

г) ${\left( {2{a^3}} \right)^4} = $  

Пр.2) Упростити следеће изразе:

а) ${\left( {{a^3}{b^5}} \right)^3} = $

б) ${\left( {{{\left( {\frac{x}{y}} \right)}^5}} \right)^8} = $

в) ${\left( {{{\left( {\frac{m}{{{n^2}}}} \right)}^2}} \right)^4} = $

г) $\frac{{{{\left( {{a^3}{b^4}} \right)}^2}}}{{a{b^5}}} = $  

Пр.3) Упростити следеће изразе:

а) ${\left( {{a^5}} \right)^2} \cdot {a^3} \cdot {\left( {{a^2}} \right)^3} = $

б) $\frac{{{x^9} \cdot {x^5}:{{\left( {{x^2}} \right)}^2}}}{{{x^8}:{x^2}}} = $

в) $\frac{{{{\left( {{x^3}} \right)}^2} \cdot {x^4}:{{\left( {{x^2}} \right)}^2}}}{{{x^6}:{{\left( {{x^4}:{x^2}} \right)}^2}}} = $

г) ${\left( {3{a^2}{b^3}} \right)^3}:3{a^4}{b^5} = $ 

Пр.4) Израчунати:

а) $\frac{{{3^7} \cdot {9^3}}}{{{{27}^3}}} = $

б) $\frac{{{2^5} \cdot {4^3}}}{{{8^4}:{{16}^2}}} = $

Пр.1) 

а) ${\left( {{m^3}} \right)^4} = {m^{3 \cdot 4}} = {m^{12}}$

б) ${\left( {{{\left( {{x^4}} \right)}^5}} \right)^6} = {x^{4 \cdot 5 \cdot 6}} = {x^{120}}$

в) ${\left( {{{\left( { - 3} \right)}^2}} \right)^7} = {\left( { - 3} \right)^{14}}$

г) ${\left( {2{a^3}} \right)^4} = {2^4} \cdot {a^{12}}$  

Пр.2)

а) ${\left( {{a^3}{b^5}} \right)^3} = {a^9}{b^{15}}$

б) ${\left( {{{\left( {\frac{x}{y}} \right)}^5}} \right)^8} = \frac{{{x^{40}}}}{{{y^{40}}}}$

в) ${\left( {{{\left( {\frac{m}{{{n^2}}}} \right)}^2}} \right)^4} = {\left( {\frac{m}{{{n^2}}}} \right)^8} = \frac{{{m^8}}}{{{n^{16}}}}$

г) $\frac{{{{\left( {{a^3}{b^4}} \right)}^2}}}{{a{b^5}}} = \frac{{{a^6}{b^8}}}{{a{b^5}}} = {a^5}{b^3}$  

Пр.3) 

а) ${\left( {{a^5}} \right)^2} \cdot {a^3} \cdot {\left( {{a^2}} \right)^3} = {a^{10}} \cdot {a^3} \cdot {a^6} = {a^{19}}$

б) $\frac{{{x^9} \cdot {x^5}:{{\left( {{x^2}} \right)}^2}}}{{{x^8}:{x^2}}} = \frac{{{x^{14}}:{x^4}}}{{{x^6}}} = \frac{{{x^{10}}}}{{{x^6}}} = {x^4}$

в) $\frac{{{{\left( {{x^3}} \right)}^2} \cdot {x^4}:{{\left( {{x^2}} \right)}^2}}}{{{x^6}:{{\left( {{x^4}:{x^2}} \right)}^2}}} = \frac{{{x^6} \cdot {x^4}:{x^4}}}{{{x^6}:{{\left( {{x^2}} \right)}^2}}} = \frac{{{x^{10}}:{x^4}}}{{{x^6}:{x^4}}} = \frac{{{x^6}}}{{{x^2}}} = {x^4}$

г) ${\left( {3{a^2}{b^3}} \right)^3}:3{a^4}{b^5} = {3^3}{a^6}{b^9}:3{a^4}{b^5} = {3^2}{a^2}{b^4} = 9{a^2}{b^4}$ 

Пр.4) 

а) $\frac{{{3^7} \cdot {9^3}}}{{{{27}^3}}} = \frac{{{3^7} \cdot {{\left( {{3^2}} \right)}^3}}}{{{{\left( {{3^3}} \right)}^3}}} = \frac{{{3^7} \cdot {3^6}}}{{{3^9}}} = \frac{{{3^{13}}}}{{{3^9}}} = {3^4} = 81 $

б) $\frac{{{2^5} \cdot {4^3}}}{{{8^4}:{{16}^2}}} = \frac{{{2^5} \cdot {{\left( {{2^2}} \right)}^3}}}{{{{\left( {{2^3}} \right)}^4}:{{\left( {{2^4}} \right)}^2}}} = \frac{{{2^5} \cdot {2^6}}}{{{2^{12}}:{2^8}}} = \frac{{{2^{11}}}}{{{2^4}}} = {2^7}$