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1. \(\left(-\dfrac{3}{2}\right)^{-3}=\left(-\dfrac{2}{3}\right)^{3}=-\dfrac{8}{27}\)
2. \(\left(-\dfrac{4}{6}\right)^5=\left(-\dfrac{2}{3}\right)^5=-\dfrac{32}{243}\)
3. \(a=\dfrac{-\frac{8}{27}}{-\frac{32}{243}}=\dfrac{8}{27}\times\dfrac{243}{32}=\dfrac{8\times 9}{32}=\dfrac{72}{32}=\dfrac{9}{4}\)

النتيجة: \(\boxed{\dfrac{9}{4}}\)

1. \(\dfrac{1}{2}+\dfrac{3}{4}-1=\dfrac{2}{4}+\dfrac{3}{4}-\dfrac{4}{4}=\dfrac{1}{4}\Rightarrow \left(\dfrac{1}{4}\right)^{-2}=16\)
2. \(\dfrac{1}{3}-\dfrac{5}{6}+1=\dfrac{2}{6}-\dfrac{5}{6}+\dfrac{6}{6}=\dfrac{3}{6}=\dfrac{1}{2}\Rightarrow \left(\dfrac{1}{2}\right)^{-2}=4\)
3. \(b=\dfrac{16}{4}=4\)

النتيجة: \(\boxed{4}\)

1. \(\dfrac{1,62}{0,18}=9 \Rightarrow \sqrt{9}=3\)
2. \(\dfrac{0,04}{10^{-4}}=\dfrac{0,04}{0,0001}=400 \Rightarrow \sqrt{400}=20\)
3. \(c=3\times 20=60\)

النتيجة: \(\boxed{60}\)

1. \(1000^{4}=(10^{3})^{4}=10^{12}\Rightarrow \dfrac{8}{1000^{4}}\times 10^{13}=8\times 10^{13-12}=8\times 10^{1}=80\)
2. \(0,0002\times 10^{7}=2\times 10^{-4}\times 10^{7}=2\times 10^{3}=2000\)
3. \(\dfrac{80}{2000}=\dfrac{1}{25}\Rightarrow d=\sqrt{\dfrac{1}{25}}=\dfrac{1}{5}\)

النتيجة: \(\boxed{\dfrac{1}{5}}\)

1. \(\left(\dfrac{3}{2}\right)^{-3}=\left(\dfrac{2}{3}\right)^{3}=\dfrac{8}{27}\)
2. \(\sqrt{\dfrac{81}{64}}=\dfrac{9}{8}\)
3. \(e=\dfrac{8}{27}\times\dfrac{9}{8}=\dfrac{9}{27}=\dfrac{1}{3}\)

النتيجة: \(\boxed{\dfrac{1}{3}}\)

1. \(\left(-\dfrac{4}{3}\right)^{2}=\dfrac{16}{9}\)
2. \(\dfrac{16}{9}\times\dfrac{9}{5}=\dfrac{16}{5}\)
3. \(5^{-1}=\dfrac{1}{5}\)
4. \(f=\dfrac{16}{5}+\dfrac{1}{5}=\dfrac{17}{5}\)

النتيجة: \(\boxed{\dfrac{17}{5}}\)

\(\sqrt{\dfrac{121}{36}}=\dfrac{\sqrt{121}}{\sqrt{36}}=\dfrac{11}{6}\)
النتيجة: \(\boxed{\dfrac{11}{6}}\)

\(\sqrt{(-2017)^{2}}=|{-2017}|=2017\)
النتيجة: \(\boxed{2017}\)

\(\left(10^{-3}\right)^{-2}=10^{(-3)\times(-2)}=10^{6}\)
النتيجة: \(\boxed{10^{6}}\)

\(5\times 5^{3}=5^{1+3}=5^{4}\Rightarrow \sqrt{5^{4}}=5^{2}=25\)
النتيجة: \(\boxed{25}\)

\(\dfrac{0,49}{0,16}=\dfrac{49/100}{16/100}=\dfrac{49}{16}\Rightarrow \sqrt{\dfrac{49}{16}}=\dfrac{7}{4}\)
النتيجة: \(\boxed{\dfrac{7}{4}}\)

\(\left(-\dfrac{2}{5}\right)^{-2}=\left(-\dfrac{5}{2}\right)^{2}=\dfrac{25}{4}\)
النتيجة: \(\boxed{\dfrac{25}{4}}\)

\(0,6=\dfrac{3}{5}\Rightarrow (0,6)^{3}=\left(\dfrac{3}{5}\right)^{3}\)
\(\left(\dfrac{3}{5}\right)^{3}\times\left(\dfrac{3}{5}\right)^{-5}=\left(\dfrac{3}{5}\right)^{3-5}=\left(\dfrac{3}{5}\right)^{-2}\)
النتيجة: \(\boxed{\left(\dfrac{3}{5}\right)^{-2}}\)

\((-4,2)^{-3}=(-1)^{-3}\times(4,2)^{-3}=- (4,2)^{-3}\)
\(- (4,2)^{-3}\times (4,2)^{4}=-(4,2)^{1}\)
و\(4,2=\dfrac{21}{5}\Rightarrow -(4,2)= -\dfrac{21}{5}=\left(-\dfrac{21}{5}\right)^{1}\)
النتيجة: \(\boxed{\left(-\dfrac{21}{5}\right)^{1}}\)

نفس القاعدة \(\Rightarrow\) نجمع الأدلة:
\(\left(-\dfrac{6}{7}\right)^{5-9}=\left(-\dfrac{6}{7}\right)^{-4}\)
النتيجة: \(\boxed{\left(-\dfrac{6}{7}\right)^{-4}}\)

\(\dfrac{9}{4}=\left(\dfrac{3}{2}\right)^{2}\Rightarrow\left(\dfrac{9}{4}\right)^{-3}=\left(\dfrac{3}{2}\right)^{-6}\)
\(\left(\dfrac{3}{2}\right)^{-6}\times\left(\dfrac{3}{2}\right)^{29}=\left(\dfrac{3}{2}\right)^{23}\)
النتيجة: \(\boxed{\left(\dfrac{3}{2}\right)^{23}}\)

\(\left[\left(\dfrac{3}{5}\right)^{4}\right]^{-14}=\left(\dfrac{3}{5}\right)^{-56}\)
\(\left(\dfrac{3}{5}\right)^{-56}\times\left(\dfrac{3}{5}\right)^{1}=\left(\dfrac{3}{5}\right)^{-55}\)
النتيجة: \(\boxed{\left(\dfrac{3}{5}\right)^{-55}}\)

\((-3)^{19}=(-1)^{19}\times 3^{19}=-3^{19}\)
\(\dfrac{-3^{19}}{3^{20}}=-\dfrac{1}{3}=(-3)^{-1}\)
النتيجة: \(\boxed{(-3)^{-1}}\)

\(\left(\dfrac{4}{25}\right)^{-2}=\left(\dfrac{25}{4}\right)^{2}=\dfrac{625}{16}\), و\(\left(\dfrac{5}{2}\right)^3=\dfrac{125}{8}\)
\(a=\dfrac{125}{8}\times\dfrac{625}{16}=\dfrac{78125}{128}\)
النتيجة: \(\boxed{\dfrac{78125}{128}}\)

\(27=3^{3}\Rightarrow 27^{-4}=3^{-12}\)
\(\left(\dfrac{1}{3}\right)^{5}=3^{-5}\Rightarrow b=3^{-5}\times 3^{-12}=3^{-17}=\dfrac{1}{3^{17}}\)
النتيجة: \(\boxed{\dfrac{1}{3^{17}}}\)

\(64\times 4=256\) و\(\dfrac{1}{4^{-4}}=4^{4}\)
\(c=256\times 4^{4}=256\times 256=65536\)
النتيجة: \(\boxed{65536}\)

\(\left(\dfrac{3}{2}\right)^{6}=\left(\dfrac{27}{8}\right)^{2}\) ولكن الأسهل:
\(\left(-\dfrac{8}{27}\right)^{3}=\left(-\dfrac{2}{3}\right)^{9}\) و\(\left(\dfrac{3}{2}\right)^{6}=\left(\dfrac{2}{3}\right)^{-6}\)
إذن \(d=\left(-\dfrac{2}{3}\right)^{9}\times\left(\dfrac{2}{3}\right)^{-6}=\left(-\dfrac{2}{3}\right)^{3}=-\dfrac{8}{27}\)
النتيجة: \(\boxed{-\dfrac{8}{27}}\)

\(9^{5}=(3^{2})^{5}=3^{10}\), و\(81=3^{4}\Rightarrow 9^{5}\times 81=3^{14}\)
\(4^{-3}=(2^{2})^{-3}=2^{-6}\)
\((2^{-2})^{-5}=2^{10}\) ثم \(2^{10}\times 2^{-2}=2^{8}\)
إذن \(e=\dfrac{3^{14}\times 2^{-6}}{2^{8}}=\dfrac{3^{14}}{2^{14}}=\left(\dfrac{3}{2}\right)^{14}\)
النتيجة: \(\boxed{\left(\dfrac{3}{2}\right)^{14}}\)

\(\left(-\dfrac{1}{5}\right)^{-2}=25\) و\(125^{3}=(5^{3})^{3}=5^{9}\)
\(f=25\times 5^{9}=5^{2}\times 5^{9}=5^{11}=48828125\)
النتيجة: \(\boxed{5^{11}}\) (أي \(\boxed{48828125}\))

عامل مشترك \(7^{-5}\):
\(g=7^{-5}(2+5)=7^{-5}\times 7=7^{-4}=\dfrac{1}{7^{4}}\)
النتيجة: \(\boxed{7^{-4}}\)

\(64=2^{6}\Rightarrow 64^{-2}=2^{-12}\)
البسط: \(2^{-12}\times 2^{4}=2^{-8}\)
المقام: \((2^{-2})^{-5}=2^{10}\) ثم \(2^{10}\times 2^{-2}=2^{8}\)
\(h=\dfrac{2^{-8}}{2^{8}}=2^{-16}=\dfrac{1}{2^{16}}\)
النتيجة: \(\boxed{2^{-16}}\)

\((2017)^{0}=1\) و\((-5)^{9}\times(-2)^{9}=\big((-5)\times(-2)\big)^{9}=10^{9}\)
النتيجة: \(\boxed{10^{9}}\)

\(1000=10^{3}\Rightarrow 10^{2}\times 10^{-5}\times 10^{3}=10^{2-5+3}=10^{0}=1\)
النتيجة: \(\boxed{1}\)

\(\sqrt{16}=4\)
النتيجة: \(\boxed{4}\)

\(\left(\dfrac{5}{2}\right)^{2}=\dfrac{25}{4}\)
النتيجة: \(\boxed{\dfrac{25}{4}}\)

\(\big(( -2)^{-2}\big)^{-2}=(-2)^{(-2)\times(-2)}=(-2)^{4}=16\)
النتيجة: \(\boxed{16}\)

\(\sqrt{\dfrac{81}{49}}=\dfrac{9}{7}\)
النتيجة: \(\boxed{\dfrac{9}{7}}\)

\(A=3^{5+11+2}=3^{18}\)
النتيجة: \(\boxed{3^{18}}\)

نفس دليل القوة: \(x^{-20}y^{-20}=(xy)^{-20}\Rightarrow B=\big((-7)\times 10\big)^{-20}=(-70)^{-20}\)
النتيجة: \(\boxed{(-70)^{-20}}\)

\(\left[10^{-11}\right]^{-2}=10^{22}\), و\(100=10^{2}\)
البسط \(=10^{2}\times 10^{22}=10^{24}\)
\(C=\dfrac{10^{24}}{10^{-15}}=10^{24-(-15)}=10^{39}\)
النتيجة: \(\boxed{10^{39}}\)

\(\left[\left(-\dfrac{2}{3}\right)^{2}\right]^{7}=\left(-\dfrac{2}{3}\right)^{14}\)
و\(\left(-\dfrac{8}{27}\right)=\left(-\dfrac{2}{3}\right)^{3}\)
إذن \(D=\left(-\dfrac{2}{3}\right)^{14+3}=\left(-\dfrac{2}{3}\right)^{17}\)
النتيجة: \(\boxed{\left(-\dfrac{2}{3}\right)^{17}}\)

\(8^{-2}=(2^{3})^{-2}=2^{-6}\) و\(\left(\dfrac{1}{5}\right)^{6}=5^{-6}\)
\(2^{-6}5^{-6}=(10)^{-6}=\left(\dfrac{1}{10}\right)^{6}\)
النتيجة: \(\boxed{\left(\dfrac{1}{10}\right)^{6}}\)

نفس دليل القوة: \(x^{-6}y^{-6}=(xy)^{-6}\)
\(\left(-\dfrac{5}{4}\right)\left(\dfrac{7}{5}\right)=-\dfrac{7}{4}\Rightarrow \left(-\dfrac{7}{4}\right)^{-6}=\left(\dfrac{4}{7}\right)^{6}\)
النتيجة: \(\boxed{\left(\dfrac{4}{7}\right)^{6}}\)

\(\left(\dfrac{2}{5}\right)^{3-9}=\left(\dfrac{2}{5}\right)^{-6}=\left(\dfrac{5}{2}\right)^{6}\)
النتيجة: \(\boxed{\left(\dfrac{5}{2}\right)^{6}}\)

\(\sqrt{\dfrac{9}{25}}=\dfrac{3}{5}=\left(\dfrac{3}{5}\right)^{1}\) و\(\dfrac{27}{125}=\left(\dfrac{3}{5}\right)^{3}\)
إذن الأدلة: \(1-14+3=-10\Rightarrow \left(\dfrac{3}{5}\right)^{-10}=\left(\dfrac{5}{3}\right)^{10}\)
النتيجة: \(\boxed{\left(\dfrac{5}{3}\right)^{10}}\)

\(\dfrac{x^{9}}{y^{9}}=\left(\dfrac{x}{y}\right)^{9}\Rightarrow \left(\dfrac{-11/3}{-5/2}\right)^{9}=\left(\dfrac{22}{15}\right)^{9}\)
النتيجة: \(\boxed{\left(\dfrac{22}{15}\right)^{9}}\)

لأن \(10\) زوجي: \(\left(-\dfrac{5}{7}\right)^{10}=\left(\dfrac{5}{7}\right)^{10}\)
إذن \(\dfrac{(5/7)^{10}}{(5/7)^{6}}=(5/7)^{4}\)
النتيجة: \(\boxed{\left(\dfrac{5}{7}\right)^{4}}\)