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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{3}{2}}\right)^{1}\\= a^{ \frac{3}{2} . 1 }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
2. \(\left(x^{\frac{2}{3}}\right)^{-1}\\= x^{ \frac{2}{3} . (-1) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
3. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-3}{5}}\\= a^{ \frac{-1}{3} . (\frac{-3}{5}) }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
4. \(\left(a^{2}\right)^{\frac{-1}{3}}\\= a^{ 2 . (\frac{-1}{3}) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
5. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-1}{2} . (\frac{-2}{5}) }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
6. \(\left(y^{\frac{3}{4}}\right)^{\frac{-1}{4}}\\= y^{ \frac{3}{4} . (\frac{-1}{4}) }= y^{\frac{-3}{16}}\\=\frac{1}{\sqrt[16]{ y^{3} }}=\frac{1}{\sqrt[16]{ y^{3} }}. \color{purple}{\frac{\sqrt[16]{ y^{13} }}{\sqrt[16]{ y^{13} }}} \\=\frac{\sqrt[16]{ y^{13} }}{|y|}\\---------------\)
7. \(\left(x^{\frac{-2}{5}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-2}{5} . (\frac{-2}{3}) }= x^{\frac{4}{15}}\\=\sqrt[15]{ x^{4} }\\---------------\)
8. \(\left(q^{-1}\right)^{1}\\= q^{ -1 . 1 }= q^{-1}\\=\frac{1}{q}\\---------------\)
9. \(\left(x^{\frac{1}{2}}\right)^{\frac{-3}{5}}\\= x^{ \frac{1}{2} . (\frac{-3}{5}) }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)
10. \(\left(a^{\frac{3}{4}}\right)^{-1}\\= a^{ \frac{3}{4} . (-1) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
11. \(\left(a^{-1}\right)^{\frac{-1}{6}}\\= a^{ -1 . (\frac{-1}{6}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
12. \(\left(q^{\frac{-3}{4}}\right)^{\frac{4}{5}}\\= q^{ \frac{-3}{4} . \frac{4}{5} }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)