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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-1}{5}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-1}{5} . (\frac{-1}{3}) }= y^{\frac{1}{15}}\\=\sqrt[15]{ y }\\---------------\)
2. \(\left(q^{1}\right)^{\frac{2}{3}}\\= q^{ 1 . \frac{2}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
3. \(\left(a^{\frac{3}{4}}\right)^{\frac{1}{2}}\\= a^{ \frac{3}{4} . \frac{1}{2} }= a^{\frac{3}{8}}\\=\sqrt[8]{ a^{3} }\\---------------\)
4. \(\left(y^{\frac{2}{5}}\right)^{\frac{1}{6}}\\= y^{ \frac{2}{5} . \frac{1}{6} }= y^{\frac{1}{15}}\\=\sqrt[15]{ y }\\---------------\)
5. \(\left(q^{\frac{1}{2}}\right)^{\frac{5}{6}}\\= q^{ \frac{1}{2} . \frac{5}{6} }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
6. \(\left(a^{-1}\right)^{\frac{3}{4}}\\= a^{ -1 . \frac{3}{4} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
7. \(\left(x^{\frac{1}{2}}\right)^{\frac{2}{5}}\\= x^{ \frac{1}{2} . \frac{2}{5} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
8. \(\left(x^{\frac{5}{4}}\right)^{1}\\= x^{ \frac{5}{4} . 1 }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
9. \(\left(q^{\frac{3}{4}}\right)^{\frac{-5}{6}}\\= q^{ \frac{3}{4} . (\frac{-5}{6}) }= q^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ q^{5} }}=\frac{1}{\sqrt[8]{ q^{5} }}. \color{purple}{\frac{\sqrt[8]{ q^{3} }}{\sqrt[8]{ q^{3} }}} \\=\frac{\sqrt[8]{ q^{3} }}{|q|}\\---------------\)
10. \(\left(q^{\frac{-1}{5}}\right)^{\frac{1}{3}}\\= q^{ \frac{-1}{5} . \frac{1}{3} }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)
11. \(\left(x^{\frac{-3}{2}}\right)^{\frac{4}{3}}\\= x^{ \frac{-3}{2} . \frac{4}{3} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
12. \(\left(q^{\frac{-3}{2}}\right)^{-2}\\= q^{ \frac{-3}{2} . (-2) }= q^{3}\\\\---------------\)