Question

с решением, если не сложно​

Answer 1

1)

${(5 \frac{2}{3} )}^{10} \times {( \frac{3}{17} )}^{10} = {(\frac{17}{3} } \times {\frac{3}{17} )}^{10} = {1}^{10} = 1$

2)

${25}^{10} \times {( \frac{1}{5}) }^{20} = {5}^{20} \times {( \frac{1}{5}) }^{20} = {(5 \times \frac{1}{5}) }^{20} = {1}^{20} = 1$

3)

${(0.5)}^{6} \times {2}^{5} = \frac{1}{2}$

4)

${(0.0016)}^{6} \times {5}^{25} = 5$

Answer 2

$\displaystyle\bf\\1) \ \Big(5\frac{2}{3}\Big)^{10} \cdot\Big(\frac{3}{17} \Big)^{10} =\underbrace{\Big(\frac{17}{3} \cdot\frac{3}{17} \Big)^{10} }_{1}=1^{10} =1\\\\\\2) \ 25^{10} \cdot\Big(\frac{1}{5} \Big)^{20} =\Big(5^{2} \Big)^{10} \cdot\Big(\frac{1}{5} \Big)^{20} =5^{20} \cdot\Big(\frac{1}{5} \Big)^{20} =\underbrace{\Big(5\cdot\frac{1}{5} \Big)^{20} } } _{1}=1\\\\\\3) \ \Big(0,5\Big)^{6} \cdot2^{5} =\Big(2^{-1} \Big)^{6}\cdot2^{5} =2^{-6} \cdot2^{5} =2^{-6+5} =2^{-1} =\frac{1}{2} =0,5$

$\displaystyle\bf\\4) \ \Big(0,0016\Big)^{6} \cdot5^{25} =\Big(0,2^{4} \Big)^{6} \cdot5^{25} =0,2^{24} \cdot5^{25} =\Big(0,2\cdot5\Big)^{24} \cdot 5=1\cdot5=5$