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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{-2}\right)^{\frac{-5}{2}}\\= q^{ -2 . (\frac{-5}{2}) }= q^{5}\\\\---------------\)
2. \(\left(y^{\frac{1}{6}}\right)^{\frac{-4}{5}}\\= y^{ \frac{1}{6} . (\frac{-4}{5}) }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
3. \(\left(q^{\frac{-1}{2}}\right)^{\frac{4}{5}}\\= q^{ \frac{-1}{2} . \frac{4}{5} }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
4. \(\left(a^{\frac{-1}{3}}\right)^{\frac{2}{3}}\\= a^{ \frac{-1}{3} . \frac{2}{3} }= a^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ a^{2} }}=\frac{1}{\sqrt[9]{ a^{2} }}. \color{purple}{\frac{\sqrt[9]{ a^{7} }}{\sqrt[9]{ a^{7} }}} \\=\frac{\sqrt[9]{ a^{7} }}{a}\\---------------\)
5. \(\left(q^{\frac{-4}{5}}\right)^{\frac{5}{2}}\\= q^{ \frac{-4}{5} . \frac{5}{2} }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
6. \(\left(a^{1}\right)^{\frac{-1}{5}}\\= a^{ 1 . (\frac{-1}{5}) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
7. \(\left(y^{\frac{1}{5}}\right)^{\frac{1}{6}}\\= y^{ \frac{1}{5} . \frac{1}{6} }= y^{\frac{1}{30}}\\=\sqrt[30]{ y }\\---------------\)
8. \(\left(q^{\frac{1}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{1}{3} . \frac{1}{2} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
9. \(\left(q^{\frac{5}{4}}\right)^{\frac{4}{3}}\\= q^{ \frac{5}{4} . \frac{4}{3} }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
10. \(\left(x^{1}\right)^{2}\\= x^{ 1 . 2 }= x^{2}\\\\---------------\)
11. \(\left(y^{\frac{2}{5}}\right)^{\frac{3}{2}}\\= y^{ \frac{2}{5} . \frac{3}{2} }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
12. \(\left(q^{\frac{3}{4}}\right)^{-1}\\= q^{ \frac{3}{4} . (-1) }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)