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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-1}{3}}\\= x^{ \frac{-1}{3} . (\frac{-1}{3}) }= x^{\frac{1}{9}}\\=\sqrt[9]{ x }\\---------------\)
2. \(\left(a^{\frac{2}{3}}\right)^{\frac{1}{5}}\\= a^{ \frac{2}{3} . \frac{1}{5} }= a^{\frac{2}{15}}\\=\sqrt[15]{ a^{2} }\\---------------\)
3. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-1}{5}}\\= y^{ \frac{-2}{5} . (\frac{-1}{5}) }= y^{\frac{2}{25}}\\=\sqrt[25]{ y^{2} }\\---------------\)
4. \(\left(y^{\frac{3}{4}}\right)^{\frac{-5}{4}}\\= y^{ \frac{3}{4} . (\frac{-5}{4}) }= y^{\frac{-15}{16}}\\=\frac{1}{\sqrt[16]{ y^{15} }}=\frac{1}{\sqrt[16]{ y^{15} }}. \color{purple}{\frac{\sqrt[16]{ y }}{\sqrt[16]{ y }}} \\=\frac{\sqrt[16]{ y }}{|y|}\\---------------\)
5. \(\left(a^{\frac{2}{3}}\right)^{1}\\= a^{ \frac{2}{3} . 1 }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
6. \(\left(x^{-1}\right)^{\frac{1}{3}}\\= x^{ -1 . \frac{1}{3} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
7. \(\left(y^{\frac{1}{2}}\right)^{\frac{-1}{2}}\\= y^{ \frac{1}{2} . (\frac{-1}{2}) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
8. \(\left(q^{-2}\right)^{2}\\= q^{ -2 . 2 }= q^{-4}\\=\frac{1}{q^{4}}\\---------------\)
9. \(\left(q^{\frac{1}{2}}\right)^{\frac{5}{3}}\\= q^{ \frac{1}{2} . \frac{5}{3} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
10. \(\left(q^{\frac{3}{4}}\right)^{\frac{2}{3}}\\= q^{ \frac{3}{4} . \frac{2}{3} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
11. \(\left(a^{\frac{-2}{3}}\right)^{1}\\= a^{ \frac{-2}{3} . 1 }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
12. \(\left(x^{\frac{1}{5}}\right)^{\frac{-3}{4}}\\= x^{ \frac{1}{5} . (\frac{-3}{4}) }= x^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ x^{3} }}=\frac{1}{\sqrt[20]{ x^{3} }}. \color{purple}{\frac{\sqrt[20]{ x^{17} }}{\sqrt[20]{ x^{17} }}} \\=\frac{\sqrt[20]{ x^{17} }}{|x|}\\---------------\)