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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{5}{2}}\right)^{\frac{5}{2}}\\= a^{ \frac{5}{2} . \frac{5}{2} }= a^{\frac{25}{4}}\\=\sqrt[4]{ a^{25} }=|a^{6}|.\sqrt[4]{ a }\\---------------\)
2. \(\left(x^{\frac{3}{5}}\right)^{1}\\= x^{ \frac{3}{5} . 1 }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
3. \(\left(q^{\frac{2}{3}}\right)^{\frac{-4}{5}}\\= q^{ \frac{2}{3} . (\frac{-4}{5}) }= q^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ q^{8} }}=\frac{1}{\sqrt[15]{ q^{8} }}. \color{purple}{\frac{\sqrt[15]{ q^{7} }}{\sqrt[15]{ q^{7} }}} \\=\frac{\sqrt[15]{ q^{7} }}{q}\\---------------\)
4. \(\left(x^{\frac{-2}{5}}\right)^{\frac{1}{4}}\\= x^{ \frac{-2}{5} . \frac{1}{4} }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
5. \(\left(y^{\frac{-1}{2}}\right)^{\frac{1}{3}}\\= y^{ \frac{-1}{2} . \frac{1}{3} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
6. \(\left(a^{\frac{1}{2}}\right)^{\frac{1}{5}}\\= a^{ \frac{1}{2} . \frac{1}{5} }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)
7. \(\left(x^{\frac{-3}{2}}\right)^{\frac{-4}{5}}\\= x^{ \frac{-3}{2} . (\frac{-4}{5}) }= x^{\frac{6}{5}}\\=\sqrt[5]{ x^{6} }=x.\sqrt[5]{ x }\\---------------\)
8. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{2} . (\frac{-1}{2}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
9. \(\left(x^{\frac{1}{3}}\right)^{\frac{3}{2}}\\= x^{ \frac{1}{3} . \frac{3}{2} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
10. \(\left(y^{-1}\right)^{\frac{-5}{6}}\\= y^{ -1 . (\frac{-5}{6}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
11. \(\left(x^{\frac{-5}{2}}\right)^{\frac{3}{2}}\\= x^{ \frac{-5}{2} . \frac{3}{2} }= x^{\frac{-15}{4}}\\=\frac{1}{\sqrt[4]{ x^{15} }}\\=\frac{1}{|x^{3}|.\sqrt[4]{ x^{3} }}=\frac{1}{|x^{3}|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{4}|}\\---------------\)
12. \(\left(x^{1}\right)^{1}\\= x^{ 1 . 1 }= x^{1}\\\\---------------\)