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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{5}{4}}\right)^{\frac{5}{2}}\\= a^{ \frac{5}{4} . \frac{5}{2} }= a^{\frac{25}{8}}\\=\sqrt[8]{ a^{25} }=|a^{3}|.\sqrt[8]{ a }\\---------------\)
2. \(\left(x^{1}\right)^{\frac{-5}{6}}\\= x^{ 1 . (\frac{-5}{6}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
3. \(\left(y^{\frac{-3}{5}}\right)^{\frac{1}{4}}\\= y^{ \frac{-3}{5} . \frac{1}{4} }= y^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ y^{3} }}=\frac{1}{\sqrt[20]{ y^{3} }}. \color{purple}{\frac{\sqrt[20]{ y^{17} }}{\sqrt[20]{ y^{17} }}} \\=\frac{\sqrt[20]{ y^{17} }}{|y|}\\---------------\)
4. \(\left(y^{\frac{3}{5}}\right)^{\frac{-2}{5}}\\= y^{ \frac{3}{5} . (\frac{-2}{5}) }= y^{\frac{-6}{25}}\\=\frac{1}{\sqrt[25]{ y^{6} }}=\frac{1}{\sqrt[25]{ y^{6} }}. \color{purple}{\frac{\sqrt[25]{ y^{19} }}{\sqrt[25]{ y^{19} }}} \\=\frac{\sqrt[25]{ y^{19} }}{y}\\---------------\)
5. \(\left(y^{\frac{1}{3}}\right)^{\frac{2}{5}}\\= y^{ \frac{1}{3} . \frac{2}{5} }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
6. \(\left(q^{1}\right)^{\frac{1}{2}}\\= q^{ 1 . \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
7. \(\left(y^{\frac{-2}{3}}\right)^{\frac{-2}{5}}\\= y^{ \frac{-2}{3} . (\frac{-2}{5}) }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
8. \(\left(x^{\frac{-1}{6}}\right)^{\frac{-5}{4}}\\= x^{ \frac{-1}{6} . (\frac{-5}{4}) }= x^{\frac{5}{24}}\\=\sqrt[24]{ x^{5} }\\---------------\)
9. \(\left(a^{\frac{-1}{2}}\right)^{-1}\\= a^{ \frac{-1}{2} . (-1) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
10. \(\left(y^{-1}\right)^{\frac{4}{5}}\\= y^{ -1 . \frac{4}{5} }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}. \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)
11. \(\left(a^{\frac{-1}{6}}\right)^{\frac{-3}{4}}\\= a^{ \frac{-1}{6} . (\frac{-3}{4}) }= a^{\frac{1}{8}}\\=\sqrt[8]{ a }\\---------------\)
12. \(\left(x^{\frac{3}{5}}\right)^{\frac{-4}{5}}\\= x^{ \frac{3}{5} . (\frac{-4}{5}) }= x^{\frac{-12}{25}}\\=\frac{1}{\sqrt[25]{ x^{12} }}=\frac{1}{\sqrt[25]{ x^{12} }}. \color{purple}{\frac{\sqrt[25]{ x^{13} }}{\sqrt[25]{ x^{13} }}} \\=\frac{\sqrt[25]{ x^{13} }}{x}\\---------------\)