Question

Rút gọn:

a) \(\dfrac{9^3}{\left(3^4-3^3\right)^2}\)

b)\(\dfrac{\left(5^4-5^3\right)^2}{1255}\)

c)\(\dfrac{32^5.81^4}{16^5.27^5}\)

d)\(\dfrac{20^{10}.81^4}{19^2.75^5}\)

e)\(\dfrac{23^3-5^5}{125}\)

f)\(\dfrac{16^4-8^5}{48}\)

Answer 1

a.

\(\dfrac{9^3}{\left(3^4-3^3\right)^2}\\ =\dfrac{3^6}{\left(3^3\left(3-1\right)\right)^2}\\ =\dfrac{3^6}{\left(3^3.2\right)^2}\\ =\dfrac{3^6}{3^6.2^4}=\dfrac{1}{2^4}\)

b.

\(\dfrac{\left(5^4-5^3\right)^2}{1255}\\ =\dfrac{\left(5^3\left(5-1\right)\right)^2}{5.251}\\ =\dfrac{\left(5^3.4\right)^2}{5.251}\\ =\dfrac{5^6.4^2}{5.251}\\ =\dfrac{5^5.4^2}{251}\)

c.

\(\dfrac{32^5.81^4}{16^5.27^5}\\ =\dfrac{2^{25}.3^{16}}{2^{20}.3^{15}}\\ =2^5.3=32.3=96\)

f.

\(\dfrac{16^4-8^5}{48}=\dfrac{2^{16}-2^{15}}{2^4.3}\\ =\dfrac{2^{15}.\left(2-1\right)}{2^4.3}\\ =\dfrac{2^{15}}{2^4.3}\\ =\dfrac{2^{11}}{3}\)