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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-3}{5}}\\= a^{ \frac{-1}{3} . (\frac{-3}{5}) }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
2. \(\left(x^{\frac{1}{5}}\right)^{\frac{4}{5}}\\= x^{ \frac{1}{5} . \frac{4}{5} }= x^{\frac{4}{25}}\\=\sqrt[25]{ x^{4} }\\---------------\)
3. \(\left(q^{\frac{-1}{2}}\right)^{\frac{3}{2}}\\= q^{ \frac{-1}{2} . \frac{3}{2} }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
4. \(\left(a^{\frac{1}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{1}{3} . (\frac{-1}{2}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
5. \(\left(y^{\frac{4}{5}}\right)^{\frac{-1}{4}}\\= y^{ \frac{4}{5} . (\frac{-1}{4}) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
6. \(\left(x^{\frac{1}{2}}\right)^{\frac{-2}{5}}\\= x^{ \frac{1}{2} . (\frac{-2}{5}) }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
7. \(\left(a^{\frac{-5}{2}}\right)^{\frac{-5}{6}}\\= a^{ \frac{-5}{2} . (\frac{-5}{6}) }= a^{\frac{25}{12}}\\=\sqrt[12]{ a^{25} }=|a^{2}|.\sqrt[12]{ a }\\---------------\)
8. \(\left(q^{\frac{-3}{4}}\right)^{\frac{3}{5}}\\= q^{ \frac{-3}{4} . \frac{3}{5} }= q^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ q^{9} }}=\frac{1}{\sqrt[20]{ q^{9} }}. \color{purple}{\frac{\sqrt[20]{ q^{11} }}{\sqrt[20]{ q^{11} }}} \\=\frac{\sqrt[20]{ q^{11} }}{|q|}\\---------------\)
9. \(\left(a^{\frac{5}{3}}\right)^{\frac{1}{2}}\\= a^{ \frac{5}{3} . \frac{1}{2} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
10. \(\left(q^{\frac{5}{6}}\right)^{1}\\= q^{ \frac{5}{6} . 1 }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
11. \(\left(y^{\frac{5}{3}}\right)^{-1}\\= y^{ \frac{5}{3} . (-1) }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
12. \(\left(q^{-1}\right)^{\frac{2}{3}}\\= q^{ -1 . \frac{2}{3} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)