Степен производа и степен количника

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Пр.1)   Упростити изразе:

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

           б) ${\left( {2ab} \right)^5} =$

           в) ${\left( {\frac{x}{y}} \right)^3} =$

Пр.2)   Израчунати:

           а) ${4^7} \cdot 0,{25^7} =$

           б) ${\left( {\frac{2}{5}} \right)^3} \cdot {5^3} \cdot {\left( {\frac{1}{4}} \right)^3} =$

           в) ${\left( { - \frac{6}{7}} \right)^4} \cdot {\left( { - 7} \right)^4} \cdot {\left( { - \frac{5}{6}} \right)^4} =$

           г) ${65^3}:{13^3} =$

           д) ${\left( { - 3\frac{2}{3}} \right)^3}:{\left( {1\frac{4}{7}} \right)^3} =$

Пр.3)   Израчунати:

           а) $\frac{{{8^3} \cdot {2^3}}}{{{4^3}}} =$

           б) $\frac{{{5^4} \cdot {2^4} \cdot 0,{1^4}}}{{0,{{25}^4}}} =$

Пр.1) 

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

           б) ${\left( {2ab} \right)^5} = {2^5}{a^5}{b^5} = 32{a^5}{b^5}$

           в) ${\left( {\frac{x}{y}} \right)^3} = \frac{{{x^3}}}{{{y^3}}}$

Пр.2)   

           а) ${4^7} \cdot {0,25^7} = {\left( {4 \cdot 0,25} \right)^7} = {1^7} = 1$

           б) ${\left( {\frac{2}{5}} \right)^3} \cdot {5^3} \cdot {\left( {\frac{1}{4}} \right)^3} = {\left( {\frac{2}{5} \cdot 5 \cdot \frac{1}{4}} \right)^3} = {\left( {\frac{1}{2}} \right)^3} = \frac{{{1^3}}}{{{2^3}}} = \frac{1}{8}$

           в) ${\left( { - \frac{6}{7}} \right)^4} \cdot {\left( { - 7} \right)^4} \cdot {\left( { - \frac{5}{6}} \right)^4} = {\left( {\left( { - \frac{6}{7}} \right) \cdot \left( { - 7} \right) \cdot \left( { - \frac{5}{6}} \right)} \right)^4} = {\left( { - 5} \right)^4} = {5^4} = 625$

           г) ${65^3}:{13^3} = {\left( {65:13} \right)^3} = {5^3} = 125$

           д) ${\left( { - 3\frac{2}{3}} \right)^3}:{\left( {1\frac{4}{7}} \right)^3} = {\left( {\left( { - 3\frac{2}{3}} \right):\left( {1\frac{4}{7}} \right)} \right)^3} = {\left( { - \frac{{11}}{3}:\frac{{11}}{7}} \right)^3} = {\left( { - \frac{{11}}{3} \cdot \frac{7}{{11}}} \right)^3} =$

$= {\left( { - \frac{7}{3}} \right)^3} = - \frac{{343}}{{27}}$

Пр.3)   

           а) $\frac{{{8^3} \cdot {2^3}}}{{{4^3}}} = \frac{{{{\left( {8 \cdot 2} \right)}^3}}}{{{4^3}}} = \frac{{{{16}^3}}}{{{4^3}}} = {\left( {\frac{{16}}{4}} \right)^3} = {4^3} = 64$

           б) $\frac{{{5^4} \cdot {2^4} \cdot {{0,1}^4}}}{{{{0,25}^4}}} = {\left( {\frac{{5 \cdot 2 \cdot 0,1}}{{0,25}}} \right)^4} = {\left( {\frac{1}{{0,25}}} \right)^4} = {\left( {\frac{{100}}{{25}}} \right)^4} = {4^4} = 256$