1.Найдите значение выражения:а) (0,6*5³-15)². б) 0,3a² при a=-18.2.Выполните действия:а)...

1.

а) $(0,6*5^3-15)^2=(\frac{6}{10}*5^3-3*5)^2=(\frac{3}{5}*5^3-3*5)^2= \\ =(3*5^2-3*5)^2=(3[5^2-5])^2= \\ =9(25-5)^2=9*20^2=9*400=3600$

б) $0,3a^2=\frac{3a^2}{10} \\ a=-18 \\ \frac{3(-18)^2}{10}=\frac{3*324}{10}=\frac{972}{10}=97,2$

2.

а) $a^{10}*a^{15}=a^{10+15}=a^{25}$

б) $a^{16}:a^{11}=a^{16-11}=a^{5}$

в) $(a^7)^3=a^{7*3}=a^{21}$

г) $(ax)^6=a^6x^6$

д) $(\frac{a}{5})^4=\frac{a^4}{5^4}=\frac{a^4}{625}$

3.

$27000=2,7*10000=2,7*10^4$

4.

а) $4a^7b^5*(-2ab^2)=4*(-2)*a^{7+1}*b^{5+2}=-8a^8b^7$

б) $(-3x^4y^2)^3=(-3)^3*x^{4*3}*y^{2*3}=-27x^{12}y^6$

в) $(-2a^5y)^2=(-2)^2*a^{5*2}*y^{1*2}=4x^{10}y^2$

5.

а) $\frac{7^9*7^{11}}{7^{18}}=\frac{7^{9+11}}{7^{18}}=\frac{7^{20}}{7^{18}}=7^{20-18}=7^2=49$

б) $\frac{5^6*125}{25^4}=\frac{5^6*5^3}{(5^2)^4}=\frac{5^{6+3}}{5^{2*4}}=\frac{5^9}{5^8}=5^{9-8}=5^1=5$

6.

а) $2\frac{2}{3}x^5y^8*(-1\frac{1}{2}x^3y^6)^2=\frac{8}{3}x^5y^8*(-\frac{3}{2}x^3y^6)^2= \\ \\ =\frac{8}{3}x^5y^8*[(-\frac{3}{2})^2*x^{3*2}*y^{6*2}]=\frac{8}{3}x^5y^8*(\frac{9}{4}*x^6*y^{12})= \\ \\ =(\frac{8}{3}*\frac{9}{4})*x^{5+6}*y^{8+12}=6x^{11}y^{20}$

б) $\frac{(a^{1+\pi})^3}{a^3}=\frac{(a^1*a^{\pi})^3}{a^3}=\frac{a^3*a^{3\pi}}{a^3}=a^{3\pi}$

Решите задачу:

$1. \\ 1)(0.6*5^{3} -15)^{2} =(0.6*125-15)^{2}=60^{2} =3600 \\ 2)0.3a^{2} \\ a=-18 \\ 0.3*(-18)^{2} = 0.3*324=97.2 \\ \\ 2. \\ 1)a ^{10} *a ^{15} =a ^{25} \\ 2)a ^{16} :a ^{11} =a ^{5} \\ 3)(a ^{7} ) ^{3} =a^{21} \\ 4)( \frac{a}{5} )^{4} = \frac{a ^{4} }{625} \\ \\ 3.27000 =2.7*10 ^{4} \\ \\$

$4. \\ \\ 1)4a ^{7} b ^{5} *(-2ab ^{2} )=-8a ^{8} b ^{7} \\ 2)(-3 x^{4} y^{2} )^{3} =-27 x^{12} y ^{6} \\ 3)(-2a^{5} y)^{2} =4a ^{10} y ^{2} \\ \\ 5.\\ 1) \frac{7 ^{9} *7 ^{11} }{7 ^{18} } = \frac{7 ^{20} }{7 ^{18} } =7 ^{2} =49 \\ 2) \frac{5 ^{6} *125}{25^{4} } = \frac{5 ^{6} *5 ^{3} }{5 ^{8} } = \frac{5^{9} }{5 ^{8} } =5^{1} =5 \\$

$6. \\ 1)2 \frac{2}{3} x^{5} y^{8} *(-1 \frac{1}{2} x^{3} y ^{6} )^{2} = \frac{8}{3} x^{5} y^{8}*(-1.5 x^{3} y ^{6} )^{2}= \\ = \frac{8}{3} x^{5} y^{8}*(2.25 x^{6} y ^{12} )=6 x^{11} y ^{20} \\ 2)(a ^{1+ \pi } ) ^{3} :a ^{3} =a ^{3} *a ^{3 \pi }:a ^{3} =a ^{3 \pi }$