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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{5}{4}}\right)^{\frac{1}{3}}\\= a^{ \frac{5}{4} . \frac{1}{3} }= a^{\frac{5}{12}}\\=\sqrt[12]{ a^{5} }\\---------------\)
2. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-5}{3}}\\= q^{ \frac{-2}{3} . (\frac{-5}{3}) }= q^{\frac{10}{9}}\\=\sqrt[9]{ q^{10} }=q.\sqrt[9]{ q }\\---------------\)
3. \(\left(q^{\frac{-2}{3}}\right)^{\frac{4}{3}}\\= q^{ \frac{-2}{3} . \frac{4}{3} }= q^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ q^{8} }}=\frac{1}{\sqrt[9]{ q^{8} }}. \color{purple}{\frac{\sqrt[9]{ q }}{\sqrt[9]{ q }}} \\=\frac{\sqrt[9]{ q }}{q}\\---------------\)
4. \(\left(x^{\frac{1}{2}}\right)^{\frac{3}{5}}\\= x^{ \frac{1}{2} . \frac{3}{5} }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
5. \(\left(y^{\frac{5}{6}}\right)^{1}\\= y^{ \frac{5}{6} . 1 }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
6. \(\left(x^{\frac{1}{4}}\right)^{\frac{5}{2}}\\= x^{ \frac{1}{4} . \frac{5}{2} }= x^{\frac{5}{8}}\\=\sqrt[8]{ x^{5} }\\---------------\)
7. \(\left(y^{-1}\right)^{-2}\\= y^{ -1 . (-2) }= y^{2}\\\\---------------\)
8. \(\left(y^{\frac{3}{2}}\right)^{\frac{5}{4}}\\= y^{ \frac{3}{2} . \frac{5}{4} }= y^{\frac{15}{8}}\\=\sqrt[8]{ y^{15} }=|y|.\sqrt[8]{ y^{7} }\\---------------\)
9. \(\left(a^{\frac{1}{5}}\right)^{\frac{-3}{5}}\\= a^{ \frac{1}{5} . (\frac{-3}{5}) }= a^{\frac{-3}{25}}\\=\frac{1}{\sqrt[25]{ a^{3} }}=\frac{1}{\sqrt[25]{ a^{3} }}. \color{purple}{\frac{\sqrt[25]{ a^{22} }}{\sqrt[25]{ a^{22} }}} \\=\frac{\sqrt[25]{ a^{22} }}{a}\\---------------\)
10. \(\left(q^{-1}\right)^{-1}\\= q^{ -1 . (-1) }= q^{1}\\\\---------------\)
11. \(\left(q^{-1}\right)^{\frac{-3}{4}}\\= q^{ -1 . (\frac{-3}{4}) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
12. \(\left(q^{-1}\right)^{\frac{-2}{3}}\\= q^{ -1 . (\frac{-2}{3}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)