Bài làm:

Bài 1

a) \(\left(x-\frac{1}{2}\right)^2=0\) 

 \(\rightarrow\left(x-\frac{1}{2}\right)^2=0^2\)

 \(\rightarrow x-\frac{1}{2}=0\) 

 \(\Rightarrow x=\frac{1}{2}\)

Bài 2

a) \(25^3\div5^2=\left(5^2\right)^3\div5^2=5^6\div5^2=5^4\)

b) \(\left(\frac{3}{7}\right)^{21}\div\left(\frac{9}{49}\right)^6=\left(\frac{3}{7}\right)^{21}\div\left[\left(\frac{3}{7}\right)^2\right]^6=\left(\frac{3}{7}\right)^{21}\div\left(\frac{3}{7}\right)^{12}=\left(\frac{3}{7}\right)^9\)

c) \(3-\left(\frac{-6}{7}\right)^0+\left(\frac{1}{2}\right)^2\div2=3-1+\frac{1}{4}\times\frac{1}{2}=2+\frac{1}{8}=\frac{17}{8}\)

Bài 3

a) \(9\times3^3\times\frac{1}{81}\times3^2=3^2\times3^3\times\frac{1}{3^4}\times3^2=3^3\)

b) \(4\times2^5\div\left(2^3\times\frac{1}{16}\right)=2^2\times2^5\div\left(2^3\times\frac{1}{2^4}\right)=2^7\div\frac{1}{2}=2^6\)

c) \(3^2\times2^5\times\left(\frac{2}{3}\right)^2=3^2\times2^5\times\frac{2^2}{3^2}=3^2\times\frac{2^7}{3^2}=2^7\)

d) \(\left(\frac{1}{3}\right)^2\times\frac{1}{3}\times9^2=\left(\frac{1}{3}\right)^3\times3^4=\frac{1}{3^3}\times3^4=3^1\)

Các bạn giải từng bước ra cho mình nhé, cảm ơn các bạn

a: \(=3^2\cdot3^5:3^4=3^{2+5-4}=3^3\)

b: \(=2^3\cdot2^4:\left(\dfrac{8}{16}\right)=\dfrac{2^7}{2}=2^6\)

c: \(=3^7\cdot3^3=3^{10}\)

d: \(=5^3\cdot5^2\cdot\dfrac{1}{5^4}=5^1\)

a: \(B=\left(4\cdot2^5\right):\left(2^3\cdot\frac{1}{16}\right)\)

\(=\left(4\cdot32\right):\left(\frac{8}{16}\right)\)

\(=128:\frac12=128\cdot2=256\)

b: \(B=3^2\cdot\frac{1}{243}\cdot81^2\cdot\frac{1}{3^3}\)

\(=3^2\cdot\frac{1}{3^5}\cdot3^8\cdot\frac{1}{3^3}=\frac{3^8}{3^8}\cdot3^2=3^2=9\)

c: \(D=\left\lbrace\left(0,1\right)^2\right\rbrace^0+\left\lbrack\left(\frac17\right)^1\right\rbrack^2:\frac{1}{49}\cdot\left\lbrack\left(2^2\right)^3:2^5\right\rbrack\)

\(=1+\left(\frac17\right)^2\cdot49\cdot2^6:2^5\)

\(=1+49\cdot\frac{1}{49}\cdot2=1+2=3\)

d: \(C=\left(-0,5\right)^5:\left(-0,5\right)^3-\left(\frac{17}{2}\right)^7:\left(\frac{17}{2}\right)^6\)

\(=\left(-0,5\right)^{5-3}-\left(\frac{17}{2}\right)\)

\(=\left(-0,5\right)^2-\frac{17}{2}=0,25-\frac{17}{2}=\frac14-\frac{34}{4}=-\frac{33}{4}\)

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

 Mình làm đc mỗi 1 câu, Thông cảm

7^6+7^5+7^4 chia hết cho 11

= 7^4.2^2+7^4.7+7^4

= 7^4.(2^2+7+1)

= 7^4. 11

Vì tích này có số 11 nên => chia hết cho 7