\(a,3^{16}:3=3^{16-1}=3^{15}\)

\(b,3^6.3^4.3^2.3=3^{6+4+2+1}=3^{13}\)

\(c,\left(-\frac{1}{4}\right).\left(6\frac{2}{11}\right)+\left(3\frac{9}{11}\right).\left(-\frac{1}{4}\right)=\left(-\frac{1}{4}\right).\frac{68}{11}+\frac{42}{11}.\left(-\frac{1}{4}\right)\)

\(=\left(-\frac{1}{4}\right)\left(\frac{68}{11}+\frac{42}{11}\right)\)

\(=\left(-\frac{1}{4}\right).10\)

\(=-\frac{10}{4}=-\frac{5}{2}\)

\(d,\left(-\frac{1}{2}\right)^3+\frac{1}{2}:5=\left(-\frac{1}{2}\right)\left(\left(\frac{1}{2}\right)^2-\frac{1}{5}\right)\)

\(=-\frac{1}{2}.\left(\frac{1}{4}-\frac{1}{5}\right)\)

\(=-\frac{1}{2}.\frac{1}{20}\)

\(=-\frac{1}{40}\)

\(g,1\frac{1}{25}+\frac{2}{21}-\frac{1}{25}+\frac{19}{21}=\frac{26}{25}+\frac{2}{21}-\frac{1}{25}+\frac{19}{21}\)

\(=\left(\frac{26}{25}-\frac{1}{25}\right)+\left(\frac{2}{21}+\frac{19}{21}\right)\)

\(=1+1\)

\(=2\)

a/

\(9.3^2.\frac{1}{81}.27=\frac{9.3^2.27}{81}=\frac{3^2.3^2.3^3}{3^4}=\frac{3^7}{3^4}=3^3\)

b/

\(4.32:\left(2^3.\frac{1}{16}\right)=4.32:\left(\frac{2^3}{16}\right)=4.32:\left(\frac{2^3}{2^4}\right)=4.32:\frac{1}{2}=4.32.2=4.64=4.4^3=4^4\)

c/

\(3^4.3^5:\frac{1}{27}=3^4.3^5.27=3^4.3^5.3^3=3^{12}\)

d/(ý bạn là (-2)^2 hay -2^2 , mình làm theo cách (-2)^2 nhé!)

\(2^2.4.\frac{32}{\left(-2\right)^2}.2^5=2^2.2^2.\frac{2^5}{2^2}.2^5=2^2.2^2.2^3.2^5=2^{12}\)

giúp minh vớ các bạn

thanks bạn thao minh donna

-8.(-2)⁵.(-2³. \(\dfrac{1}{16}\)) = 256 . \(\dfrac{-1}{2}\) = -128 = (-2)⁷

Bài 6: 

a: \(2^{27}=8^9\)

\(3^{18}=9^9\)

b: Vì \(8^9< 9^9\)

nên \(2^{27}< 3^{18}\)

Ta có: +) \({({2^2})^3} = {2^2}{.2^2}{.2^2} = {2^{2 + 2 + 2}} = {2^6}\)

+) \({\left[ {{{( - 3)}^2}} \right]^2} = {( - 3)^2}.{( - 3)^2} = {( - 3)^{2 + 2}} = {( - 3)^4}\)

Câu 3 :

A = 7776 . 8 - 2.243. 64

A = 62208 - 31104

A = 31104

Câu 1 :

a) \(12^5=3^5.4^5\)

b) \(20^6=4^6.5^6\)

c) \(54^3=6^3.9^3\)

Câu 2 :

a) \(3.5^{55}=3.\left(5^5\right)^{11}\)

b) \(4.3^{816}=4.\left(3^{17}\right)^{48}\)

c) \(9.8.7^{6412}=9.8.\left(7^{28}\right)^{229}\)

a) 5^3 x 5^6

= 5^3+6

= 5^9

b) 3^4 x 3

= 3^4+1

= 3^5

nha bn

a) 5³ . 5⁶ = 5⁹ ; b) 3⁴ . 3 = 3⁵

a ) 5³.5⁶

= 5³⁺⁶

= 5⁹

b ) 3^4.3

= 3¹²

Answer : a ) 5⁹

b ) 3¹²