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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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