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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-4}{3}}\\= x^{ \frac{-2}{3} . (\frac{-4}{3}) }= x^{\frac{8}{9}}\\=\sqrt[9]{ x^{8} }\\---------------\)
2. \(\left(y^{\frac{-3}{2}}\right)^{2}\\= y^{ \frac{-3}{2} . 2 }= y^{-3}\\=\frac{1}{y^{3}}\\---------------\)
3. \(\left(q^{\frac{-1}{4}}\right)^{\frac{-1}{6}}\\= q^{ \frac{-1}{4} . (\frac{-1}{6}) }= q^{\frac{1}{24}}\\=\sqrt[24]{ q }\\---------------\)
4. \(\left(q^{\frac{-1}{5}}\right)^{\frac{3}{5}}\\= q^{ \frac{-1}{5} . \frac{3}{5} }= q^{\frac{-3}{25}}\\=\frac{1}{\sqrt[25]{ q^{3} }}=\frac{1}{\sqrt[25]{ q^{3} }}. \color{purple}{\frac{\sqrt[25]{ q^{22} }}{\sqrt[25]{ q^{22} }}} \\=\frac{\sqrt[25]{ q^{22} }}{q}\\---------------\)
5. \(\left(y^{\frac{4}{5}}\right)^{\frac{5}{2}}\\= y^{ \frac{4}{5} . \frac{5}{2} }= y^{2}\\\\---------------\)
6. \(\left(y^{\frac{1}{5}}\right)^{\frac{1}{3}}\\= y^{ \frac{1}{5} . \frac{1}{3} }= y^{\frac{1}{15}}\\=\sqrt[15]{ y }\\---------------\)
7. \(\left(x^{\frac{-1}{4}}\right)^{1}\\= x^{ \frac{-1}{4} . 1 }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
8. \(\left(q^{\frac{-1}{4}}\right)^{\frac{1}{2}}\\= q^{ \frac{-1}{4} . \frac{1}{2} }= q^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ q }}=\frac{1}{\sqrt[8]{ q }}. \color{purple}{\frac{\sqrt[8]{ q^{7} }}{\sqrt[8]{ q^{7} }}} \\=\frac{\sqrt[8]{ q^{7} }}{|q|}\\---------------\)
9. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-3}{2}}\\= y^{ \frac{-2}{3} . (\frac{-3}{2}) }= y^{1}\\\\---------------\)
10. \(\left(y^{2}\right)^{\frac{-1}{2}}\\= y^{ 2 . (\frac{-1}{2}) }= y^{-1}\\=\frac{1}{y}\\---------------\)
11. \(\left(x^{\frac{-1}{5}}\right)^{\frac{-5}{2}}\\= x^{ \frac{-1}{5} . (\frac{-5}{2}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
12. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-5}{6}}\\= y^{ \frac{-1}{2} . (\frac{-5}{6}) }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)