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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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