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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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