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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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