Tìm x, biết: a) x : (-1/2)^3 = -1/2; b) x . (3/5)^7 = (3/5)^9;

Câu hỏi:

Tìm x, biết:

$a) x:{\left(\frac{-1}{2}\right)}^3=\frac{-1}{2}$

b) $x.{\left(\frac{3}{5}\right)}^7={\left(\frac{3}{5}\right)}^9$

c) ${\left(\frac{-2}{3}\right)}^{11}:x={\left(\frac{-2}{3}\right)}^9$

d) $x.{\left(0,25\right)}^6={\left(\frac{1}{4}\right)}^8$

Trả lời:

$$\begin{gathered} a) x:{\left(\frac{-1}{2}\right)}^3=\frac{-1}{2} \\ x:\frac{{\left(-1\right)}^3}{2^3}=\frac{-1}{2} \\ x:\frac{-1}{8}=\frac{-1}{2} \\ x=\frac{-1}{2}.\frac{-1}{8} \\ x=\frac{1}{16} \end{gathered}$$

Vậy $x=\frac{1}{16}$

$$\begin{gathered} b) x.{\left(\frac{3}{5}\right)}^7={\left(\frac{3}{5}\right)}^9 \\ x={\left(\frac{3}{5}\right)}^9:{\left(\frac{3}{5}\right)}^7 \\ x={\left(\frac{3}{5}\right)}^{9-7} \\ x={\left(\frac{3}{5}\right)}^2=\frac{9}{25} \\ Vậy x=\frac{9}{25} \end{gathered}$$

$$\begin{gathered} c) {\left(\frac{-2}{3}\right)}^{11}:x={\left(\frac{-2}{3}\right)}^9 \\ x={\left(\frac{-2}{3}\right)}^{11}:{\left(\frac{-2}{3}\right)}^9 \\ x={\left(\frac{-2}{3}\right)}^{11-9} \\ x={\left(\frac{-2}{3}\right)}^2=\frac{4}{9} \\ Vậy x=\frac{4}{9} \end{gathered}$$

$$\begin{gathered} d) x.{\left(0,25\right)}^6={\left(\frac{1}{4}\right)}^8 \\ x.{\left(\frac{1}{4}\right)}^6={\left(\frac{1}{4}\right)}^8 \\ x={\left(\frac{1}{4}\right)}^8:{\left(\frac{1}{4}\right)}^6 \\ x={\left(\frac{1}{4}\right)}^{8-6} \\ x={\left(\frac{1}{4}\right)}^2=\frac{1}{16} \\ Vậy x=\frac{1}{16} \end{gathered}$$