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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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