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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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