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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{3}{2}}\right)^{2}\\= x^{ \frac{3}{2} . 2 }= x^{3}\\\\---------------\)
2. \(\left(q^{\frac{2}{3}}\right)^{\frac{-1}{6}}\\= q^{ \frac{2}{3} . (\frac{-1}{6}) }= q^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ q }}=\frac{1}{\sqrt[9]{ q }}. \color{purple}{\frac{\sqrt[9]{ q^{8} }}{\sqrt[9]{ q^{8} }}} \\=\frac{\sqrt[9]{ q^{8} }}{q}\\---------------\)
3. \(\left(x^{\frac{-4}{5}}\right)^{\frac{1}{2}}\\= x^{ \frac{-4}{5} . \frac{1}{2} }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
4. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-5}{3}}\\= x^{ \frac{-1}{2} . (\frac{-5}{3}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
5. \(\left(y^{\frac{-1}{5}}\right)^{\frac{-5}{6}}\\= y^{ \frac{-1}{5} . (\frac{-5}{6}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
6. \(\left(a^{\frac{-3}{5}}\right)^{\frac{-3}{4}}\\= a^{ \frac{-3}{5} . (\frac{-3}{4}) }= a^{\frac{9}{20}}\\=\sqrt[20]{ a^{9} }\\---------------\)
7. \(\left(y^{\frac{-1}{2}}\right)^{1}\\= y^{ \frac{-1}{2} . 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
8. \(\left(a^{\frac{-2}{3}}\right)^{-1}\\= a^{ \frac{-2}{3} . (-1) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
9. \(\left(x^{\frac{1}{2}}\right)^{1}\\= x^{ \frac{1}{2} . 1 }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
10. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-2}{3}}\\= a^{ \frac{-1}{3} . (\frac{-2}{3}) }= a^{\frac{2}{9}}\\=\sqrt[9]{ a^{2} }\\---------------\)
11. \(\left(a^{-1}\right)^{\frac{-3}{5}}\\= a^{ -1 . (\frac{-3}{5}) }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
12. \(\left(q^{\frac{-2}{5}}\right)^{1}\\= q^{ \frac{-2}{5} . 1 }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)