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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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