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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{2}{3}}\right)^{\frac{2}{3}}\\= a^{ \frac{2}{3} . \frac{2}{3} }= a^{\frac{4}{9}}\\=\sqrt[9]{ a^{4} }\\---------------\)
2. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{3} . (\frac{-1}{2}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
3. \(\left(y^{\frac{-3}{5}}\right)^{\frac{2}{3}}\\= y^{ \frac{-3}{5} . \frac{2}{3} }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
4. \(\left(x^{\frac{-3}{2}}\right)^{1}\\= x^{ \frac{-3}{2} . 1 }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
5. \(\left(q^{1}\right)^{\frac{-2}{3}}\\= q^{ 1 . (\frac{-2}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
6. \(\left(a^{-1}\right)^{\frac{1}{2}}\\= a^{ -1 . \frac{1}{2} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
7. \(\left(q^{2}\right)^{-1}\\= q^{ 2 . (-1) }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
8. \(\left(x^{\frac{-1}{5}}\right)^{\frac{2}{5}}\\= x^{ \frac{-1}{5} . \frac{2}{5} }= x^{\frac{-2}{25}}\\=\frac{1}{\sqrt[25]{ x^{2} }}=\frac{1}{\sqrt[25]{ x^{2} }}. \color{purple}{\frac{\sqrt[25]{ x^{23} }}{\sqrt[25]{ x^{23} }}} \\=\frac{\sqrt[25]{ x^{23} }}{x}\\---------------\)
9. \(\left(y^{\frac{-5}{6}}\right)^{\frac{1}{2}}\\= y^{ \frac{-5}{6} . \frac{1}{2} }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
10. \(\left(x^{\frac{-3}{4}}\right)^{1}\\= x^{ \frac{-3}{4} . 1 }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
11. \(\left(a^{\frac{-1}{5}}\right)^{\frac{4}{5}}\\= a^{ \frac{-1}{5} . \frac{4}{5} }= a^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ a^{4} }}=\frac{1}{\sqrt[25]{ a^{4} }}. \color{purple}{\frac{\sqrt[25]{ a^{21} }}{\sqrt[25]{ a^{21} }}} \\=\frac{\sqrt[25]{ a^{21} }}{a}\\---------------\)
12. \(\left(a^{\frac{2}{5}}\right)^{\frac{5}{4}}\\= a^{ \frac{2}{5} . \frac{5}{4} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)