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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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