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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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