Question

Tính và so sánh :

a) \(\left(\frac{-2}{3}\right)^3\) và \(\frac{\left(-2\right)^3}{3^3}\)

b) \(\frac{10^5}{2^5}\)và \(\left(\frac{10}{2}\right)^5\)

Answer 1

a) 

\(\left(-\frac{2}{3}\right)^3=\frac{\left(-2\right)^3}{3^3}\)

mà \(\frac{\left(-2\right)^3}{3^3}\) là vế phải 

\(\Rightarrow\) \(\left(-\frac{2}{3}\right)^3=\frac{\left(-2\right)^3}{3^3}\) 

b) 

\(\frac{10^5}{2^5}=\left(\frac{10}{2}\right)^5\)

mà \(\left(\frac{10}{2}\right)^5\) là vế phải 

Nên \(\frac{10^5}{2^5}=\left(\frac{10}{2}\right)^5\)

Answer 2

a) \(\left(-\frac{2}{3}\right)^3=\left(-\frac{2}{3}\right).\left(-\frac{2}{3}\right).\left(-\frac{2}{3}\right)=\frac{\left(-2\right).\left(-2\right).\left(-2\right)}{3.3.3}=\frac{\left(-2\right)^3}{3^3}=\frac{-8}{27}\)

b) \(\left(\frac{10}{2}\right)^5=\frac{10}{2}.\frac{10}{2}.\frac{10}{2}.\frac{10}{2}.\frac{10}{2}=\frac{10.10.10.10.10}{2.2.2.2.2}=\frac{10^5}{2^5}=\frac{100000}{32}=3125\)