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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-1}{6} . (\frac{-2}{5}) }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)
2. \(\left(y^{\frac{-1}{5}}\right)^{\frac{1}{3}}\\= y^{ \frac{-1}{5} . \frac{1}{3} }= y^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ y }}=\frac{1}{\sqrt[15]{ y }}. \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y}\\---------------\)
3. \(\left(a^{\frac{-3}{2}}\right)^{\frac{-1}{6}}\\= a^{ \frac{-3}{2} . (\frac{-1}{6}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
4. \(\left(x^{\frac{5}{3}}\right)^{\frac{1}{3}}\\= x^{ \frac{5}{3} . \frac{1}{3} }= x^{\frac{5}{9}}\\=\sqrt[9]{ x^{5} }\\---------------\)
5. \(\left(a^{\frac{-3}{4}}\right)^{\frac{-3}{2}}\\= a^{ \frac{-3}{4} . (\frac{-3}{2}) }= a^{\frac{9}{8}}\\=\sqrt[8]{ a^{9} }=|a|.\sqrt[8]{ a }\\---------------\)
6. \(\left(q^{\frac{-1}{3}}\right)^{\frac{2}{3}}\\= q^{ \frac{-1}{3} . \frac{2}{3} }= q^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ q^{2} }}=\frac{1}{\sqrt[9]{ q^{2} }}. \color{purple}{\frac{\sqrt[9]{ q^{7} }}{\sqrt[9]{ q^{7} }}} \\=\frac{\sqrt[9]{ q^{7} }}{q}\\---------------\)
7. \(\left(y^{\frac{-5}{3}}\right)^{2}\\= y^{ \frac{-5}{3} . 2 }= y^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ y^{10} }}\\=\frac{1}{y^{3}.\sqrt[3]{ y }}=\frac{1}{y^{3}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{4}}\\---------------\)
8. \(\left(q^{\frac{-2}{5}}\right)^{\frac{-3}{5}}\\= q^{ \frac{-2}{5} . (\frac{-3}{5}) }= q^{\frac{6}{25}}\\=\sqrt[25]{ q^{6} }\\---------------\)
9. \(\left(a^{\frac{-3}{2}}\right)^{\frac{4}{3}}\\= a^{ \frac{-3}{2} . \frac{4}{3} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
10. \(\left(x^{-1}\right)^{1}\\= x^{ -1 . 1 }= x^{-1}\\=\frac{1}{x}\\---------------\)
11. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-3}{4}}\\= y^{ \frac{-1}{2} . (\frac{-3}{4}) }= y^{\frac{3}{8}}\\=\sqrt[8]{ y^{3} }\\---------------\)
12. \(\left(x^{\frac{3}{5}}\right)^{\frac{4}{3}}\\= x^{ \frac{3}{5} . \frac{4}{3} }= x^{\frac{4}{5}}\\=\sqrt[5]{ x^{4} }\\---------------\)