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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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