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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-5}{3}}\\= a^{ \frac{-1}{3} . (\frac{-5}{3}) }= a^{\frac{5}{9}}\\=\sqrt[9]{ a^{5} }\\---------------\)
2. \(\left(a^{\frac{2}{3}}\right)^{\frac{1}{2}}\\= a^{ \frac{2}{3} . \frac{1}{2} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
3. \(\left(y^{\frac{2}{5}}\right)^{\frac{-2}{5}}\\= y^{ \frac{2}{5} . (\frac{-2}{5}) }= y^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ y^{4} }}=\frac{1}{\sqrt[25]{ y^{4} }}. \color{purple}{\frac{\sqrt[25]{ y^{21} }}{\sqrt[25]{ y^{21} }}} \\=\frac{\sqrt[25]{ y^{21} }}{y}\\---------------\)
4. \(\left(y^{\frac{-4}{5}}\right)^{\frac{2}{3}}\\= y^{ \frac{-4}{5} . \frac{2}{3} }= y^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ y^{8} }}=\frac{1}{\sqrt[15]{ y^{8} }}. \color{purple}{\frac{\sqrt[15]{ y^{7} }}{\sqrt[15]{ y^{7} }}} \\=\frac{\sqrt[15]{ y^{7} }}{y}\\---------------\)
5. \(\left(y^{\frac{1}{3}}\right)^{1}\\= y^{ \frac{1}{3} . 1 }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
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. \(\left(a^{\frac{-4}{5}}\right)^{-1}\\= a^{ \frac{-4}{5} . (-1) }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)
8. \(\left(x^{\frac{4}{3}}\right)^{\frac{-3}{2}}\\= x^{ \frac{4}{3} . (\frac{-3}{2}) }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
9. \(\left(q^{\frac{-1}{4}}\right)^{\frac{1}{2}}\\= q^{ \frac{-1}{4} . \frac{1}{2} }= q^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ q }}=\frac{1}{\sqrt[8]{ q }}. \color{purple}{\frac{\sqrt[8]{ q^{7} }}{\sqrt[8]{ q^{7} }}} \\=\frac{\sqrt[8]{ q^{7} }}{|q|}\\---------------\)
10. \(\left(x^{\frac{-5}{3}}\right)^{\frac{2}{3}}\\= x^{ \frac{-5}{3} . \frac{2}{3} }= x^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ x^{10} }}\\=\frac{1}{x.\sqrt[9]{ x }}=\frac{1}{x.\sqrt[9]{ x }} \color{purple}{\frac{\sqrt[9]{ x^{8} }}{\sqrt[9]{ x^{8} }}} \\=\frac{\sqrt[9]{ x^{8} }}{x^{2}}\\---------------\)
11. \(\left(q^{\frac{-2}{3}}\right)^{\frac{4}{3}}\\= q^{ \frac{-2}{3} . \frac{4}{3} }= q^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ q^{8} }}=\frac{1}{\sqrt[9]{ q^{8} }}. \color{purple}{\frac{\sqrt[9]{ q }}{\sqrt[9]{ q }}} \\=\frac{\sqrt[9]{ q }}{q}\\---------------\)
12. \(\left(x^{\frac{3}{2}}\right)^{\frac{-4}{3}}\\= x^{ \frac{3}{2} . (\frac{-4}{3}) }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)