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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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