Question

как найти знач. выр-я? 1) 3 ^5/6 * 9^ 1/12 2)7 ^3,8/49^1,4 3) 2^3,2* 6^6,2 / 12^5,2 4) 4^4 *3^9:12^4 5)9* 4√125 * 12√125 6) 20 √5* 5√5 / 4√5 7) (36^6) ^3/ (6^4)^8 8) (5^4/7 * 11 ^2/3 /55^12)^21

Answer 1

$3^{ \frac{5}{6} } * 9^{ \frac{1}{12} }= 3^{ \frac{5}{6} }* 3^{ \frac{2}{12} }=3^{ \frac{5}{6} }* 3^{ \frac{1}{6} }=3$

$\frac{ 7^{3.8} }{ 49^{1.4} } = \frac{ 7^{3.8} }{ 7^{2.8} } =7^1=7$

$\frac{ 2^{3.2} * 6^{6.2} }{ 12^{5.2} } = \frac{ 2^{3.2} * 6^{6.2} }{ 2^{5.2} * 6^{5.2} } = \frac{6}{2^2} = \frac{6}{4} =1.5$

$\frac{4^4*3^9}{12^4} = \frac{4^4*3^9}{3^4*4^4} =3^5=243$

$9*4 \sqrt{125} *12 \sqrt{125} =36*125*12=54000$

$\frac{20 \sqrt{5} *5 \sqrt{5} }{4 \sqrt{5} } =25 \sqrt{5}$

$\frac{(36*6)^3}{(6*4)^8} = \frac{6^9}{6^8*4^8} = \frac{6}{4^8} = \frac{2*3}{ 2^{16} } = \frac{3}{ 2^{15} }$

$( \frac{ 5^{ \frac{4}{7} }* 11^{ \frac{2}{3} }}{ 55^{12} })^{21} = \frac{ 5^{12} * 11^{14} }{ 5^{252} * 11^{252} } = 5^{-240} * 11^{-238}$