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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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