تمارين القوى مع التصحيحات المفصلة
\[ a = \sqrt{\frac{81}{16}} \]
💡 إظهار الحل
\( a = \sqrt{\frac{81}{16}} \)
\( = \frac{\sqrt{81}}{\sqrt{16}} \)
\( = \frac{9}{4} \)
\[ b = (-2)^8 \times (2017)^0 \times (-5)^8 \]
💡 إظهار الحل
\( b = (-2)^8 \times (2017)^0 \times (-5)^8 \)
\( = (2^8) \times 1 \times (5^8) \)
\( = 2^8 \times 5^8 \)
\( = (2 \times 5)^8 \)
\( = 10^8 \)
\[ c = \sqrt{\frac{75}{27}} \div 3^{-2} \]
💡 إظهار الحل
\( c = \sqrt{\frac{75}{27}} \div 3^{-2} \)
\( = \sqrt{\frac{25 \times 3}{9 \times 3}} \div 3^{-2} \)
\( = \sqrt{\frac{25}{9}} \div 3^{-2} \)
\( = \frac{5}{3} \div 3^{-2} \)
\( = \frac{5}{3} \times 3^{2} \)
\( = \frac{5}{3} \times 9 \)
\( = 15 \)
\[ d = \frac{2}{3} \left( \frac{2}{3} \right)^3 \]
💡 إظهار الحل
\( d = \frac{2}{3} \times \left( \frac{2}{3} \right)^3 \)
\( = \left( \frac{2}{3} \right)^1 \times \left( \frac{2}{3} \right)^3 \)
\( = \left( \frac{2}{3} \right)^{1+3} \)
\( = \left( \frac{2}{3} \right)^4 \)
\( = \frac{2^4}{3^4} \)
\( = \frac{16}{81} \)