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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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