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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-3}{4}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-3}{4} . (\frac{-4}{3}) }= a^{1}\\\\---------------\)
2. \(\left(q^{\frac{1}{2}}\right)^{\frac{-5}{3}}\\= q^{ \frac{1}{2} . (\frac{-5}{3}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
3. \(\left(y^{\frac{2}{3}}\right)^{\frac{-1}{5}}\\= y^{ \frac{2}{3} . (\frac{-1}{5}) }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
4. \(\left(a^{\frac{-1}{5}}\right)^{\frac{3}{4}}\\= a^{ \frac{-1}{5} . \frac{3}{4} }= a^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ a^{3} }}=\frac{1}{\sqrt[20]{ a^{3} }}. \color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a|}\\---------------\)
5. \(\left(q^{\frac{5}{2}}\right)^{\frac{-4}{3}}\\= q^{ \frac{5}{2} . (\frac{-4}{3}) }= q^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ q^{10} }}\\=\frac{1}{q^{3}.\sqrt[3]{ q }}=\frac{1}{q^{3}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{4}}\\---------------\)
6. \(\left(q^{\frac{-2}{5}}\right)^{-1}\\= q^{ \frac{-2}{5} . (-1) }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
7. \(\left(y^{\frac{4}{3}}\right)^{\frac{2}{5}}\\= y^{ \frac{4}{3} . \frac{2}{5} }= y^{\frac{8}{15}}\\=\sqrt[15]{ y^{8} }\\---------------\)
8. \(\left(a^{\frac{1}{4}}\right)^{-1}\\= a^{ \frac{1}{4} . (-1) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
9. \(\left(x^{\frac{1}{2}}\right)^{\frac{1}{2}}\\= x^{ \frac{1}{2} . \frac{1}{2} }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
10. \(\left(x^{2}\right)^{\frac{-2}{5}}\\= x^{ 2 . (\frac{-2}{5}) }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)
11. \(\left(y^{\frac{1}{3}}\right)^{1}\\= y^{ \frac{1}{3} . 1 }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
12. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-1}{2} . (\frac{-1}{2}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)