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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-5}{4}}\right)^{\frac{3}{4}}\\= y^{ \frac{-5}{4} . \frac{3}{4} }= y^{\frac{-15}{16}}\\=\frac{1}{\sqrt[16]{ y^{15} }}=\frac{1}{\sqrt[16]{ y^{15} }}. \color{purple}{\frac{\sqrt[16]{ y }}{\sqrt[16]{ y }}} \\=\frac{\sqrt[16]{ y }}{|y|}\\---------------\)
2. \(\left(x^{\frac{-2}{3}}\right)^{\frac{1}{3}}\\= x^{ \frac{-2}{3} . \frac{1}{3} }= x^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ x^{2} }}=\frac{1}{\sqrt[9]{ x^{2} }}. \color{purple}{\frac{\sqrt[9]{ x^{7} }}{\sqrt[9]{ x^{7} }}} \\=\frac{\sqrt[9]{ x^{7} }}{x}\\---------------\)
3. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-2}{3} . (\frac{-1}{2}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
4. \(\left(q^{-1}\right)^{\frac{-2}{5}}\\= q^{ -1 . (\frac{-2}{5}) }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
5. \(\left(q^{\frac{1}{4}}\right)^{\frac{-1}{3}}\\= q^{ \frac{1}{4} . (\frac{-1}{3}) }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
6. \(\left(x^{\frac{-2}{3}}\right)^{\frac{1}{5}}\\= x^{ \frac{-2}{3} . \frac{1}{5} }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
7. \(\left(a^{\frac{2}{3}}\right)^{\frac{-3}{2}}\\= a^{ \frac{2}{3} . (\frac{-3}{2}) }= a^{-1}\\=\frac{1}{a}\\---------------\)
8. \(\left(q^{\frac{3}{5}}\right)^{\frac{5}{4}}\\= q^{ \frac{3}{5} . \frac{5}{4} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
9. \(\left(x^{-1}\right)^{2}\\= x^{ -1 . 2 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
10. \(\left(a^{\frac{2}{3}}\right)^{\frac{1}{5}}\\= a^{ \frac{2}{3} . \frac{1}{5} }= a^{\frac{2}{15}}\\=\sqrt[15]{ a^{2} }\\---------------\)
11. \(\left(a^{\frac{1}{5}}\right)^{\frac{-3}{5}}\\= a^{ \frac{1}{5} . (\frac{-3}{5}) }= a^{\frac{-3}{25}}\\=\frac{1}{\sqrt[25]{ a^{3} }}=\frac{1}{\sqrt[25]{ a^{3} }}. \color{purple}{\frac{\sqrt[25]{ a^{22} }}{\sqrt[25]{ a^{22} }}} \\=\frac{\sqrt[25]{ a^{22} }}{a}\\---------------\)
12. \(\left(q^{\frac{2}{5}}\right)^{\frac{-1}{3}}\\= q^{ \frac{2}{5} . (\frac{-1}{3}) }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)