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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{5}{3}}\right)^{\frac{1}{5}}\\= x^{ \frac{5}{3} . \frac{1}{5} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
2. \(\left(q^{\frac{-3}{4}}\right)^{\frac{3}{4}}\\= q^{ \frac{-3}{4} . \frac{3}{4} }= q^{\frac{-9}{16}}\\=\frac{1}{\sqrt[16]{ q^{9} }}=\frac{1}{\sqrt[16]{ q^{9} }}. \color{purple}{\frac{\sqrt[16]{ q^{7} }}{\sqrt[16]{ q^{7} }}} \\=\frac{\sqrt[16]{ q^{7} }}{|q|}\\---------------\)
3. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-1}{6}}\\= x^{ \frac{-2}{3} . (\frac{-1}{6}) }= x^{\frac{1}{9}}\\=\sqrt[9]{ x }\\---------------\)
4. \(\left(y^{1}\right)^{\frac{-5}{6}}\\= y^{ 1 . (\frac{-5}{6}) }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
5. \(\left(a^{\frac{-2}{3}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-2}{3} . (\frac{-1}{3}) }= a^{\frac{2}{9}}\\=\sqrt[9]{ a^{2} }\\---------------\)
6. \(\left(q^{1}\right)^{-1}\\= q^{ 1 . (-1) }= q^{-1}\\=\frac{1}{q}\\---------------\)
7. \(\left(q^{\frac{-1}{6}}\right)^{-1}\\= q^{ \frac{-1}{6} . (-1) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
8. \(\left(q^{\frac{1}{6}}\right)^{\frac{-3}{2}}\\= q^{ \frac{1}{6} . (\frac{-3}{2}) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
9. \(\left(x^{\frac{4}{5}}\right)^{\frac{-3}{5}}\\= x^{ \frac{4}{5} . (\frac{-3}{5}) }= x^{\frac{-12}{25}}\\=\frac{1}{\sqrt[25]{ x^{12} }}=\frac{1}{\sqrt[25]{ x^{12} }}. \color{purple}{\frac{\sqrt[25]{ x^{13} }}{\sqrt[25]{ x^{13} }}} \\=\frac{\sqrt[25]{ x^{13} }}{x}\\---------------\)
10. \(\left(y^{\frac{-1}{2}}\right)^{-1}\\= y^{ \frac{-1}{2} . (-1) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
11. \(\left(y^{\frac{4}{5}}\right)^{\frac{1}{3}}\\= y^{ \frac{4}{5} . \frac{1}{3} }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
12. \(\left(q^{\frac{-2}{3}}\right)^{\frac{5}{2}}\\= q^{ \frac{-2}{3} . \frac{5}{2} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)