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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{1}\right)^{2}\\= x^{ 1 . 2 }= x^{2}\\\\---------------\)
2. \(\left(q^{\frac{-2}{3}}\right)^{\frac{5}{3}}\\= q^{ \frac{-2}{3} . \frac{5}{3} }= q^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ q^{10} }}\\=\frac{1}{q.\sqrt[9]{ q }}=\frac{1}{q.\sqrt[9]{ q }} \color{purple}{\frac{\sqrt[9]{ q^{8} }}{\sqrt[9]{ q^{8} }}} \\=\frac{\sqrt[9]{ q^{8} }}{q^{2}}\\---------------\)
3. \(\left(q^{\frac{-3}{5}}\right)^{\frac{-1}{4}}\\= q^{ \frac{-3}{5} . (\frac{-1}{4}) }= q^{\frac{3}{20}}\\=\sqrt[20]{ q^{3} }\\---------------\)
4. \(\left(x^{-1}\right)^{\frac{1}{5}}\\= x^{ -1 . \frac{1}{5} }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
5. \(\left(a^{1}\right)^{\frac{3}{2}}\\= a^{ 1 . \frac{3}{2} }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
6. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-1}{4}}\\= q^{ \frac{-1}{2} . (\frac{-1}{4}) }= q^{\frac{1}{8}}\\=\sqrt[8]{ q }\\---------------\)
7. \(\left(q^{\frac{-1}{4}}\right)^{\frac{1}{5}}\\= q^{ \frac{-1}{4} . \frac{1}{5} }= q^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ q }}=\frac{1}{\sqrt[20]{ q }}. \color{purple}{\frac{\sqrt[20]{ q^{19} }}{\sqrt[20]{ q^{19} }}} \\=\frac{\sqrt[20]{ q^{19} }}{|q|}\\---------------\)
8. \(\left(a^{\frac{-3}{2}}\right)^{\frac{5}{4}}\\= a^{ \frac{-3}{2} . \frac{5}{4} }= a^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ a^{15} }}\\=\frac{1}{|a|.\sqrt[8]{ a^{7} }}=\frac{1}{|a|.\sqrt[8]{ a^{7} }} \color{purple}{\frac{\sqrt[8]{ a }}{\sqrt[8]{ a }}} \\=\frac{\sqrt[8]{ a }}{|a^{2}|}\\---------------\)
9. \(\left(q^{\frac{3}{5}}\right)^{-1}\\= q^{ \frac{3}{5} . (-1) }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
10. \(\left(q^{\frac{1}{2}}\right)^{\frac{-1}{3}}\\= q^{ \frac{1}{2} . (\frac{-1}{3}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
11. \(\left(q^{\frac{-5}{4}}\right)^{\frac{5}{4}}\\= q^{ \frac{-5}{4} . \frac{5}{4} }= q^{\frac{-25}{16}}\\=\frac{1}{\sqrt[16]{ q^{25} }}\\=\frac{1}{|q|.\sqrt[16]{ q^{9} }}=\frac{1}{|q|.\sqrt[16]{ q^{9} }} \color{purple}{\frac{\sqrt[16]{ q^{7} }}{\sqrt[16]{ q^{7} }}} \\=\frac{\sqrt[16]{ q^{7} }}{|q^{2}|}\\---------------\)
12. \(\left(a^{\frac{4}{5}}\right)^{\frac{1}{3}}\\= a^{ \frac{4}{5} . \frac{1}{3} }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)