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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{2}{3}}\right)^{\frac{2}{3}}\\= q^{ \frac{2}{3} . \frac{2}{3} }= q^{\frac{4}{9}}\\=\sqrt[9]{ q^{4} }\\---------------\)
2. \(\left(x^{\frac{-1}{3}}\right)^{\frac{1}{5}}\\= x^{ \frac{-1}{3} . \frac{1}{5} }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)
3. \(\left(x^{\frac{1}{2}}\right)^{\frac{3}{5}}\\= x^{ \frac{1}{2} . \frac{3}{5} }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
4. \(\left(x^{\frac{-2}{3}}\right)^{-1}\\= x^{ \frac{-2}{3} . (-1) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
5. \(\left(x^{\frac{-5}{4}}\right)^{-1}\\= x^{ \frac{-5}{4} . (-1) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
6. \(\left(y^{\frac{-2}{3}}\right)^{\frac{1}{5}}\\= y^{ \frac{-2}{3} . \frac{1}{5} }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
7. \(\left(q^{\frac{-3}{5}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-3}{5} . (\frac{-2}{5}) }= q^{\frac{6}{25}}\\=\sqrt[25]{ q^{6} }\\---------------\)
8. \(\left(y^{\frac{3}{5}}\right)^{\frac{3}{2}}\\= y^{ \frac{3}{5} . \frac{3}{2} }= y^{\frac{9}{10}}\\=\sqrt[10]{ y^{9} }\\---------------\)
9. \(\left(a^{\frac{-1}{2}}\right)^{\frac{3}{4}}\\= a^{ \frac{-1}{2} . \frac{3}{4} }= a^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ a^{3} }}=\frac{1}{\sqrt[8]{ a^{3} }}. \color{purple}{\frac{\sqrt[8]{ a^{5} }}{\sqrt[8]{ a^{5} }}} \\=\frac{\sqrt[8]{ a^{5} }}{|a|}\\---------------\)
10. \(\left(q^{\frac{-4}{3}}\right)^{\frac{-5}{3}}\\= q^{ \frac{-4}{3} . (\frac{-5}{3}) }= q^{\frac{20}{9}}\\=\sqrt[9]{ q^{20} }=q^{2}.\sqrt[9]{ q^{2} }\\---------------\)
11. \(\left(y^{\frac{3}{5}}\right)^{\frac{-5}{3}}\\= y^{ \frac{3}{5} . (\frac{-5}{3}) }= y^{-1}\\=\frac{1}{y}\\---------------\)
12. \(\left(a^{\frac{2}{3}}\right)^{\frac{1}{3}}\\= a^{ \frac{2}{3} . \frac{1}{3} }= a^{\frac{2}{9}}\\=\sqrt[9]{ a^{2} }\\---------------\)