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Werk uit m.b.v. de rekenregels

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

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