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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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