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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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