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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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