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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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