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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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