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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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