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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{1}\right)^{\frac{-3}{5}}\\= q^{ 1 . (\frac{-3}{5}) }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
2. \(\left(q^{\frac{-5}{6}}\right)^{\frac{1}{3}}\\= q^{ \frac{-5}{6} . \frac{1}{3} }= q^{\frac{-5}{18}}\\=\frac{1}{\sqrt[18]{ q^{5} }}=\frac{1}{\sqrt[18]{ q^{5} }}. \color{purple}{\frac{\sqrt[18]{ q^{13} }}{\sqrt[18]{ q^{13} }}} \\=\frac{\sqrt[18]{ q^{13} }}{|q|}\\---------------\)
3. \(\left(a^{\frac{-1}{5}}\right)^{\frac{-3}{5}}\\= a^{ \frac{-1}{5} . (\frac{-3}{5}) }= a^{\frac{3}{25}}\\=\sqrt[25]{ a^{3} }\\---------------\)
4. \(\left(y^{1}\right)^{-2}\\= y^{ 1 . (-2) }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
5. \(\left(q^{2}\right)^{-1}\\= q^{ 2 . (-1) }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
6. \(\left(x^{\frac{1}{2}}\right)^{1}\\= x^{ \frac{1}{2} . 1 }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
7. \(\left(q^{\frac{1}{4}}\right)^{\frac{-1}{3}}\\= q^{ \frac{1}{4} . (\frac{-1}{3}) }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
8. \(\left(y^{\frac{3}{2}}\right)^{\frac{1}{3}}\\= y^{ \frac{3}{2} . \frac{1}{3} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
9. \(\left(y^{\frac{-1}{3}}\right)^{-1}\\= y^{ \frac{-1}{3} . (-1) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
10. \(\left(q^{\frac{1}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{1}{2} . \frac{1}{2} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
11. \(\left(x^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= x^{ \frac{-1}{2} . \frac{1}{2} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
12. \(\left(x^{\frac{5}{6}}\right)^{\frac{1}{3}}\\= x^{ \frac{5}{6} . \frac{1}{3} }= x^{\frac{5}{18}}\\=\sqrt[18]{ x^{5} }\\---------------\)