Question

Rút gọn biểu thức:

a) 2^7 . 9^3/ 6^5.8^2

b) 6^3 + 3.6^2 +3^3 / -13

c) 5^4 . 20^4/ 25^4 . 4^5

d) (5^4.5^3)^3/125^4

e) Căn ( 2,5 - 0,7)^2

f) Căn 3^2 + căn 39^2/ căn 7^2 + căn 91^2

Answer 1

a) \(\frac{2^7\cdot9^3}{6^5\cdot8^2}=\frac{2^7\cdot\left(3^2\right)^3}{\left(2\cdot3\right)^5\cdot\left(2^3\right)^2}=\frac{2^7\cdot3^6}{2^5\cdot3^5\cdot2^6}=\frac{3}{2^4}=\frac{3}{16}\)

c) \(\frac{5^4\cdot20^4}{25^4\cdot4^5}=\frac{5^4\cdot\left(2^2\cdot5\right)^4}{\left(5^2\right)^4\cdot\left(2^2\right)^5}=\frac{5^4\cdot2^8\cdot5^4}{5^8\cdot2^{10}}=\frac{1}{2^2}=\frac{1}{4}\)

d) \(\frac{\left(5^4\cdot20^4\right)^3}{125^4}=\frac{5^{12}\cdot20^{12}}{\left(5^3\right)^4}=\frac{5^{12}\cdot\left(2^2\cdot5\right)^{12}}{5^{12}}=2^{24}\cdot5^{12}\)