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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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