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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{1}{2}}\right)^{\frac{-5}{4}}\\= q^{ \frac{1}{2} . (\frac{-5}{4}) }= q^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ q^{5} }}=\frac{1}{\sqrt[8]{ q^{5} }}. \color{purple}{\frac{\sqrt[8]{ q^{3} }}{\sqrt[8]{ q^{3} }}} \\=\frac{\sqrt[8]{ q^{3} }}{|q|}\\---------------\)
2. \(\left(x^{\frac{-2}{5}}\right)^{\frac{1}{2}}\\= x^{ \frac{-2}{5} . \frac{1}{2} }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
3. \(\left(y^{\frac{-3}{2}}\right)^{\frac{-1}{5}}\\= y^{ \frac{-3}{2} . (\frac{-1}{5}) }= y^{\frac{3}{10}}\\=\sqrt[10]{ y^{3} }\\---------------\)
4. \(\left(y^{\frac{-5}{4}}\right)^{\frac{-5}{4}}\\= y^{ \frac{-5}{4} . (\frac{-5}{4}) }= y^{\frac{25}{16}}\\=\sqrt[16]{ y^{25} }=|y|.\sqrt[16]{ y^{9} }\\---------------\)
5. \(\left(y^{\frac{3}{5}}\right)^{\frac{2}{3}}\\= y^{ \frac{3}{5} . \frac{2}{3} }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
6. \(\left(q^{\frac{1}{4}}\right)^{1}\\= q^{ \frac{1}{4} . 1 }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
7. \(\left(y^{-2}\right)^{-2}\\= y^{ -2 . (-2) }= y^{4}\\\\---------------\)
8. \(\left(a^{\frac{-1}{6}}\right)^{\frac{1}{4}}\\= a^{ \frac{-1}{6} . \frac{1}{4} }= a^{\frac{-1}{24}}\\=\frac{1}{\sqrt[24]{ a }}=\frac{1}{\sqrt[24]{ a }}. \color{purple}{\frac{\sqrt[24]{ a^{23} }}{\sqrt[24]{ a^{23} }}} \\=\frac{\sqrt[24]{ a^{23} }}{|a|}\\---------------\)
9. \(\left(a^{\frac{2}{5}}\right)^{\frac{-1}{3}}\\= a^{ \frac{2}{5} . (\frac{-1}{3}) }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
10. \(\left(y^{-1}\right)^{\frac{2}{3}}\\= y^{ -1 . \frac{2}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
11. \(\left(q^{\frac{2}{3}}\right)^{\frac{3}{4}}\\= q^{ \frac{2}{3} . \frac{3}{4} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
12. \(\left(x^{\frac{5}{4}}\right)^{\frac{4}{3}}\\= x^{ \frac{5}{4} . \frac{4}{3} }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)