Question

1/ Tính:

a) \(\left(1+\frac{2}{3}-\frac{1}{4}\right).\left(\frac{4}{5}-\frac{3}{4}\right)^2\)

b) \(2\div\left(\frac{1}{2}-\frac{2}{3}\right)^3\)

2/ Tìm số tự nhiên n, biết:

a) \(\frac{16}{2^n}=2\); b) \(\frac{\left(-3\right)^n}{81}=-27\); c) \(8^n:2^n=4\)

Answer 1

1.a.\(\left(1+\frac{2}{3}-\frac{1}{4}\right).\left(\frac{4}{5}-\frac{3}{4}\right)^2=\frac{17}{12}.\left(\frac{1}{20}\right)^2=\frac{17}{12}.\frac{1}{400}=\frac{17}{4800}\)

b. \(2\div\left(\frac{1}{2}-\frac{2}{3}\right)^3=2\div\left(-\frac{1}{6}\right)^3=2\div\left(-\frac{1}{216}\right)=2.\left(-216\right)=-432\)

2.a.\(\frac{16}{2^n}=2\Rightarrow2^n=16:2=8=2^3\Rightarrow n=3\)

b.\(\frac{\left(-3\right)^n}{81}=-27\Rightarrow\left(-3\right)^n=-27.81=-2187=\left(-3\right)^7\Rightarrow n=7\)

c. \(8^n:2^n=4\Rightarrow\left(8:2\right)^n=4\Rightarrow4^n=4^1\Rightarrow n=1\)