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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{5}{4}}\right)^{\frac{1}{4}}\\= a^{ \frac{5}{4} . \frac{1}{4} }= a^{\frac{5}{16}}\\=\sqrt[16]{ a^{5} }\\---------------\)
2. \(\left(q^{\frac{3}{2}}\right)^{\frac{-1}{4}}\\= q^{ \frac{3}{2} . (\frac{-1}{4}) }= q^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ q^{3} }}=\frac{1}{\sqrt[8]{ q^{3} }}. \color{purple}{\frac{\sqrt[8]{ q^{5} }}{\sqrt[8]{ q^{5} }}} \\=\frac{\sqrt[8]{ q^{5} }}{|q|}\\---------------\)
3. \(\left(x^{1}\right)^{\frac{5}{6}}\\= x^{ 1 . \frac{5}{6} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
4. \(\left(q^{\frac{-2}{3}}\right)^{-1}\\= q^{ \frac{-2}{3} . (-1) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
5. \(\left(x^{\frac{3}{2}}\right)^{\frac{1}{5}}\\= x^{ \frac{3}{2} . \frac{1}{5} }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
6. \(\left(a^{\frac{3}{5}}\right)^{\frac{-4}{3}}\\= a^{ \frac{3}{5} . (\frac{-4}{3}) }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)
7. \(\left(a^{\frac{5}{3}}\right)^{\frac{-3}{5}}\\= a^{ \frac{5}{3} . (\frac{-3}{5}) }= a^{-1}\\=\frac{1}{a}\\---------------\)
8. \(\left(q^{2}\right)^{1}\\= q^{ 2 . 1 }= q^{2}\\\\---------------\)
9. \(\left(a^{\frac{-1}{5}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-1}{5} . (\frac{-4}{3}) }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
10. \(\left(a^{-1}\right)^{\frac{-1}{3}}\\= a^{ -1 . (\frac{-1}{3}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
11. \(\left(a^{\frac{4}{5}}\right)^{\frac{5}{2}}\\= a^{ \frac{4}{5} . \frac{5}{2} }= a^{2}\\\\---------------\)
12. \(\left(q^{\frac{3}{5}}\right)^{2}\\= q^{ \frac{3}{5} . 2 }= q^{\frac{6}{5}}\\=\sqrt[5]{ q^{6} }=q.\sqrt[5]{ q }\\---------------\)