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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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