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Werk uit m.b.v. de rekenregels

1. \(\left(x^{\frac{3}{2}}\right)^{\frac{-5}{4}}\)
2. \(\left(x^{\frac{1}{2}}\right)^{\frac{-5}{6}}\)
3. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-1}{5}}\)
4. \(\left(x^{1}\right)^{-2}\)
5. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-1}{3}}\)
6. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\)
7. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-3}{4}}\)
8. \(\left(a^{\frac{5}{6}}\right)^{\frac{1}{4}}\)
9. \(\left(x^{\frac{5}{2}}\right)^{\frac{-1}{3}}\)
10. \(\left(a^{\frac{2}{3}}\right)^{\frac{-3}{4}}\)
11. \(\left(a^{\frac{-1}{4}}\right)^{\frac{3}{4}}\)
12. \(\left(x^{\frac{1}{2}}\right)^{\frac{-3}{5}}\)

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{3}{2}}\right)^{\frac{-5}{4}}\\= x^{ \frac{3}{2} . (\frac{-5}{4}) }= x^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ x^{15} }}\\=\frac{1}{|x|.\sqrt[8]{ x^{7} }}=\frac{1}{|x|.\sqrt[8]{ x^{7} }} \color{purple}{\frac{\sqrt[8]{ x }}{\sqrt[8]{ x }}} \\=\frac{\sqrt[8]{ x }}{|x^{2}|}\\---------------\)
2. \(\left(x^{\frac{1}{2}}\right)^{\frac{-5}{6}}\\= x^{ \frac{1}{2} . (\frac{-5}{6}) }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
3. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-1}{5}}\\= q^{ \frac{-1}{6} . (\frac{-1}{5}) }= q^{\frac{1}{30}}\\=\sqrt[30]{ q }\\---------------\)
4. \(\left(x^{1}\right)^{-2}\\= x^{ 1 . (-2) }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
5. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-1}{3}}\\= x^{ \frac{-1}{2} . (\frac{-1}{3}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
6. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-2}{3} . (\frac{-1}{2}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
7. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-3}{4}}\\= y^{ \frac{-2}{3} . (\frac{-3}{4}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
8. \(\left(a^{\frac{5}{6}}\right)^{\frac{1}{4}}\\= a^{ \frac{5}{6} . \frac{1}{4} }= a^{\frac{5}{24}}\\=\sqrt[24]{ a^{5} }\\---------------\)
9. \(\left(x^{\frac{5}{2}}\right)^{\frac{-1}{3}}\\= x^{ \frac{5}{2} . (\frac{-1}{3}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
10. \(\left(a^{\frac{2}{3}}\right)^{\frac{-3}{4}}\\= a^{ \frac{2}{3} . (\frac{-3}{4}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
11. \(\left(a^{\frac{-1}{4}}\right)^{\frac{3}{4}}\\= a^{ \frac{-1}{4} . \frac{3}{4} }= a^{\frac{-3}{16}}\\=\frac{1}{\sqrt[16]{ a^{3} }}=\frac{1}{\sqrt[16]{ a^{3} }}. \color{purple}{\frac{\sqrt[16]{ a^{13} }}{\sqrt[16]{ a^{13} }}} \\=\frac{\sqrt[16]{ a^{13} }}{|a|}\\---------------\)
12. \(\left(x^{\frac{1}{2}}\right)^{\frac{-3}{5}}\\= x^{ \frac{1}{2} . (\frac{-3}{5}) }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)