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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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