Question

[Lê Thanh Thúy]

Bài 1: Thực hiện phép tính:

a) \(\left(\frac{3}{5}\right)^2-[\frac{1}{3}:3-\sqrt{16}.\left(\frac{1}{2}\right)^2]-\left(10\times12-2014\right)^0\)

b)\(|-\frac{100}{123}|:\left(\frac{3}{4}+\frac{7}{12}\right)+\frac{23}{123}:\left(\frac{9}{5}-\frac{7}{15}\right)\)

c) \(\frac{\left(-5\right)^{32}\times20^{43}}{\left(-8\right)^{29}\times125^{25}}\)

Bài 2: Tìm x biết

a)\(\frac{2}{3}-\left(\frac{3}{4}-x\right)=\sqrt{\frac{1}{9}}\)

b) \(\left(\frac{1}{2}-x\right)^2=\left(-2\right)^2\)

c) \(|3x+\frac{1}{2}|-\frac{2}{3}=1\)

d) \(3^{2x+1}=81\)

Answer 1

[Akai Haruma]

Bài 1:

a)

\((\frac{3}{5})^2-[\frac{1}{3}:3-\sqrt{16}.(\frac{1}{2})^2]-(10.12-2014)^0\)

\(=\frac{9}{25}-(\frac{1}{9}-1)-1\)

\(=\frac{9}{25}-\frac{1}{9}=\frac{56}{225}\)

b)

\(|-\frac{100}{123}|:(\frac{3}{4}+\frac{7}{12})+\frac{23}{123}:(\frac{9}{5}-\frac{7}{15})\)

\(=\frac{100}{123}:\frac{4}{3}+\frac{23}{123}:\frac{4}{3}=(\frac{100}{123}+\frac{23}{123}):\frac{4}{3}=1:\frac{4}{3}=\frac{3}{4}\)

c)

\(\frac{(-5)^{32}.20^{43}}{(-8)^{29}.125^{25}}=\frac{5^{32}.(2^2.5)^{43}}{(-2)^{3.29}.(5^3)^{25}}=\frac{5^{32}.2^{86}.5^{43}}{-2^{87}.5^{75}}\)

\(=\frac{5^{32+43}.2^{86}}{-2^{87}.5^{75}}=\frac{5^{75}.2^{86}}{-2^{87}.5^{75}}=-\frac{1}{2}\)

Answer 2

[Akai Haruma]

Bài 2:

a)

\(\frac{2}{3}-(\frac{3}{4}-x)=\sqrt{\frac{1}{9}}=\frac{1}{3}\)

\(\frac{3}{4}-x=\frac{2}{3}-\frac{1}{3}=\frac{1}{3}\)

\(x=\frac{3}{4}-\frac{1}{3}=\frac{5}{12}\)

b)

\((\frac{1}{2}-x)^2=(-2)^2=2^2\)

\(\Rightarrow \left[\begin{matrix} \frac{1}{2}-x=-2\\ \frac{1}{2}-x=2\end{matrix}\right.\Rightarrow \left[\begin{matrix} x=\frac{5}{2}\\ x=\frac{-3}{2}\end{matrix}\right.\)

c)

\(|3x+\frac{1}{2}|-\frac{2}{3}=1\)

\(|3x+\frac{1}{2}|=\frac{2}{3}+1=\frac{5}{3}\)

\(\Rightarrow \left[\begin{matrix} 3x+\frac{1}{2}=\frac{5}{3}\\ 3x+\frac{1}{2}=-\frac{5}{3}\end{matrix}\right.\Rightarrow \left[\begin{matrix} x=\frac{7}{18}\\ x=\frac{-13}{18}\end{matrix}\right.\)

d)

\(3^{2x+1}=81=3^4\)

\(\Rightarrow 2x+1=4\Rightarrow x=\frac{3}{2}\)