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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-3}{5}}\right)^{\frac{3}{5}}\\= y^{ \frac{-3}{5} . \frac{3}{5} }= y^{\frac{-9}{25}}\\=\frac{1}{\sqrt[25]{ y^{9} }}=\frac{1}{\sqrt[25]{ y^{9} }}. \color{purple}{\frac{\sqrt[25]{ y^{16} }}{\sqrt[25]{ y^{16} }}} \\=\frac{\sqrt[25]{ y^{16} }}{y}\\---------------\)
2. \(\left(a^{1}\right)^{2}\\= a^{ 1 . 2 }= a^{2}\\\\---------------\)
3. \(\left(q^{\frac{3}{5}}\right)^{\frac{4}{3}}\\= q^{ \frac{3}{5} . \frac{4}{3} }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
4. \(\left(q^{-2}\right)^{\frac{-5}{4}}\\= q^{ -2 . (\frac{-5}{4}) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
5. \(\left(y^{\frac{-3}{5}}\right)^{\frac{1}{3}}\\= y^{ \frac{-3}{5} . \frac{1}{3} }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
6. \(\left(a^{\frac{-1}{6}}\right)^{\frac{-2}{3}}\\= a^{ \frac{-1}{6} . (\frac{-2}{3}) }= a^{\frac{1}{9}}\\=\sqrt[9]{ a }\\---------------\)
7. \(\left(q^{\frac{3}{2}}\right)^{\frac{5}{3}}\\= q^{ \frac{3}{2} . \frac{5}{3} }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
8. \(\left(x^{\frac{-4}{5}}\right)^{\frac{5}{4}}\\= x^{ \frac{-4}{5} . \frac{5}{4} }= x^{-1}\\=\frac{1}{x}\\---------------\)
9. \(\left(y^{\frac{2}{5}}\right)^{\frac{1}{6}}\\= y^{ \frac{2}{5} . \frac{1}{6} }= y^{\frac{1}{15}}\\=\sqrt[15]{ y }\\---------------\)
10. \(\left(q^{\frac{-1}{3}}\right)^{\frac{-2}{5}}\\= q^{ \frac{-1}{3} . (\frac{-2}{5}) }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
11. \(\left(y^{\frac{3}{2}}\right)^{\frac{1}{5}}\\= y^{ \frac{3}{2} . \frac{1}{5} }= y^{\frac{3}{10}}\\=\sqrt[10]{ y^{3} }\\---------------\)
12. \(\left(y^{\frac{-5}{6}}\right)^{\frac{3}{5}}\\= y^{ \frac{-5}{6} . \frac{3}{5} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)