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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-5}{6}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-5}{6} . (\frac{-4}{3}) }= a^{\frac{10}{9}}\\=\sqrt[9]{ a^{10} }=a.\sqrt[9]{ a }\\---------------\)
2. \(\left(a^{\frac{3}{4}}\right)^{\frac{1}{2}}\\= a^{ \frac{3}{4} . \frac{1}{2} }= a^{\frac{3}{8}}\\=\sqrt[8]{ a^{3} }\\---------------\)
3. \(\left(a^{\frac{1}{3}}\right)^{\frac{-4}{5}}\\= a^{ \frac{1}{3} . (\frac{-4}{5}) }= a^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ a^{4} }}=\frac{1}{\sqrt[15]{ a^{4} }}. \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a}\\---------------\)
4. \(\left(y^{\frac{4}{5}}\right)^{\frac{-3}{5}}\\= y^{ \frac{4}{5} . (\frac{-3}{5}) }= y^{\frac{-12}{25}}\\=\frac{1}{\sqrt[25]{ y^{12} }}=\frac{1}{\sqrt[25]{ y^{12} }}. \color{purple}{\frac{\sqrt[25]{ y^{13} }}{\sqrt[25]{ y^{13} }}} \\=\frac{\sqrt[25]{ y^{13} }}{y}\\---------------\)
5. \(\left(y^{\frac{2}{5}}\right)^{\frac{3}{2}}\\= y^{ \frac{2}{5} . \frac{3}{2} }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
6. \(\left(a^{\frac{2}{3}}\right)^{-1}\\= a^{ \frac{2}{3} . (-1) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
7. \(\left(y^{\frac{5}{2}}\right)^{\frac{-1}{3}}\\= y^{ \frac{5}{2} . (\frac{-1}{3}) }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
8. \(\left(q^{\frac{-4}{3}}\right)^{\frac{-1}{4}}\\= q^{ \frac{-4}{3} . (\frac{-1}{4}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
9. \(\left(x^{\frac{1}{2}}\right)^{1}\\= x^{ \frac{1}{2} . 1 }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
10. \(\left(y^{\frac{-1}{4}}\right)^{\frac{3}{5}}\\= y^{ \frac{-1}{4} . \frac{3}{5} }= y^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ y^{3} }}=\frac{1}{\sqrt[20]{ y^{3} }}. \color{purple}{\frac{\sqrt[20]{ y^{17} }}{\sqrt[20]{ y^{17} }}} \\=\frac{\sqrt[20]{ y^{17} }}{|y|}\\---------------\)
11. \(\left(x^{\frac{2}{5}}\right)^{\frac{-1}{5}}\\= x^{ \frac{2}{5} . (\frac{-1}{5}) }= x^{\frac{-2}{25}}\\=\frac{1}{\sqrt[25]{ x^{2} }}=\frac{1}{\sqrt[25]{ x^{2} }}. \color{purple}{\frac{\sqrt[25]{ x^{23} }}{\sqrt[25]{ x^{23} }}} \\=\frac{\sqrt[25]{ x^{23} }}{x}\\---------------\)
12. \(\left(y^{1}\right)^{-1}\\= y^{ 1 . (-1) }= y^{-1}\\=\frac{1}{y}\\---------------\)