Question

Bài 1) Rút gọn biểu thức

a) \(\frac{2^7.9^3}{6^5.8^2}\) 

b) \(\frac{6^3+3.6^2+3^3}{-13}\) 

c) \(\frac{5^4.20^4}{25^5.4^5}\) 

d)(\(\frac{5^4-5^3}{125^4}\) )

Answer 1

a.

\(\frac{2^7\times9^3}{6^5\times8^2}=\frac{2^7\times\left(3^2\right)^3}{\left(2\times3\right)^5\times\left(2^3\right)^2}=\frac{2^7\times3^6}{2^5\times3^5\times2^6}=\frac{3}{2^4}=\frac{3}{16}\)

b.

\(\frac{6^3+3\times6^2+3^3}{-13}=\frac{\left(2\times3\right)^3+3\times\left(3\times2\right)^2+3^3}{-13}=\frac{2^3\times3^3+3\times3^2\times2^2+3^3}{-13}=\frac{8\times3^3+3^3\times4+3^3}{-13}\)\(=\frac{3^3\times\left(8+4+1\right)}{-13}=\frac{27\times13}{-13}=-27\)

c.

\(\frac{5^4\times20^4}{25^5\times4^5}=\frac{\left(5\times20\right)^4}{\left(25\times4\right)^5}=\frac{100^4}{100^5}=\frac{1}{100}\)

d.

\(\left(\frac{5^4-5^3}{125^4}\right)=\frac{5^3\times\left(5-1\right)}{\left(5^3\right)^4}=\frac{5^3\times4}{5^{12}}=\frac{4}{5^9}\)

Answer 2

a)\(\frac{2^7.9^3}{6^5.8^2}=\frac{2^7.\left(3^2\right)^3}{2^5.3^5.\left(2^3\right)^2}=\frac{2^7.3^6}{2^5.3^5.2^6}=\frac{3}{2^4}\)

b)\(\frac{6^3+3.6^2+3^3}{-13}=\frac{6.6^2+3.6^2+3^3}{-13}=\frac{6^2.\left(6+3\right)+3^3}{-13}=\frac{6^2.9+3^3}{-13}=\frac{6^2.3^2+3.3^2}{-13}=\frac{3^2.\left(6^2+3\right)}{-13}=\frac{3^2.39}{-13}=3^2.\left(-3\right)=-27\)

c)\(\frac{5^4.20^4}{25^5.4^5}=\frac{100^4}{100^5}=\frac{1}{100}\)

 

 

Answer 3

làm nhanh giùm mình nha mình đang cần gấp

Answer 4

a)2^7*9^3/6^5*8^2=2^7*(3^2)^3/(2*3)^5*(2^3)^5* (2^3)^2=2^7*3^6/2^5*3^5*2^6=3/2^4=3/16 b)6^3+3*6^2+3^3/-13=(2*3)^3+3*(2*3)^2+3^3/-13=2^3*3^3+3*2^3*3^3+3^3/-13=8*3^3+3^3*4+3^3*1/-13=3^3*(8+4+1)/-13=27*13/-13=-27 c)5^4*20^4/25^4*4^5=5^4*(4*5)^4/(5*5)^5)4^5=5^4*4^4*5^4/5^5*5^5*4^5=5^0*4^0*5^0/5^1*5^1*4^1=1/5*5*4=1/100