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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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