أكمل العمليات التالية:
- $(\frac{5}{2})^{-3} \times (\frac{5}{2})^{....} = (\frac{5}{2})^{-1}$
- $\sqrt{\frac{162}{8}} = .......$
- $(......)^2 = 81$
- $-2^5 = .........$
الحل: 🛠️
- $(\frac{5}{2})^{-3} \times (\frac{5}{2})^{\mathbf{2}} = (\frac{5}{2})^{-3+2} = (\frac{5}{2})^{-1}$
- $\sqrt{\frac{162}{8}} = \sqrt{\frac{81}{4}} = \mathbf{\frac{9}{2} = 4,5}$
- $(\mathbf{9})^2 = 81$ أو $(\mathbf{-9})^2 = 81$
- $-2^5 = -(2 \times 2 \times 2 \times 2 \times 2) = \mathbf{-32}$
$A = -\frac{5}{2} + \frac{1}{2} \times \frac{4}{5}$
$A = -\frac{5}{2} + \frac{1 \times 4}{2 \times 5} = -\frac{5}{2} + \frac{4}{10}$
$A = -\frac{25}{10} + \frac{4}{10} = -\frac{21}{10} = -2,1$ ✅
$C = 3^{-1} \times 21 - \sqrt{25} \times 5^{-1}$
$C = \frac{1}{3} \times 21 - 5 \times \frac{1}{5}$
$C = 7 - 1 = 6$ ✅
$b = \frac{16}{25} \times (-\frac{5}{4})^5$
$b = (\frac{4}{5})^2 \times (-\frac{5}{4})^5 = (\frac{5}{4})^{-2} \times (-\frac{5}{4})^5$
$b = -(\frac{5}{4})^{-2+5} = -(\frac{5}{4})^3$ ✅