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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{1}\right)^{\frac{-2}{5}}\\= q^{ 1 . (\frac{-2}{5}) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
2. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-1}{6}}\\= q^{ \frac{-1}{2} . (\frac{-1}{6}) }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)
3. \(\left(a^{\frac{-3}{4}}\right)^{\frac{5}{4}}\\= a^{ \frac{-3}{4} . \frac{5}{4} }= a^{\frac{-15}{16}}\\=\frac{1}{\sqrt[16]{ a^{15} }}=\frac{1}{\sqrt[16]{ a^{15} }}. \color{purple}{\frac{\sqrt[16]{ a }}{\sqrt[16]{ a }}} \\=\frac{\sqrt[16]{ a }}{|a|}\\---------------\)
4. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{2} . (\frac{-1}{2}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
5. \(\left(x^{\frac{4}{5}}\right)^{\frac{-5}{3}}\\= x^{ \frac{4}{5} . (\frac{-5}{3}) }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
6. \(\left(x^{\frac{4}{3}}\right)^{\frac{-5}{4}}\\= x^{ \frac{4}{3} . (\frac{-5}{4}) }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
7. \(\left(q^{\frac{-1}{3}}\right)^{\frac{5}{2}}\\= q^{ \frac{-1}{3} . \frac{5}{2} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
8. \(\left(q^{\frac{-2}{5}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-2}{5} . (\frac{-1}{2}) }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
9. \(\left(y^{\frac{-1}{4}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{4} . (\frac{-1}{2}) }= y^{\frac{1}{8}}\\=\sqrt[8]{ y }\\---------------\)
10. \(\left(q^{\frac{1}{4}}\right)^{-1}\\= q^{ \frac{1}{4} . (-1) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
11. \(\left(a^{\frac{3}{4}}\right)^{\frac{-1}{5}}\\= a^{ \frac{3}{4} . (\frac{-1}{5}) }= a^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ a^{3} }}=\frac{1}{\sqrt[20]{ a^{3} }}. \color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a|}\\---------------\)
12. \(\left(q^{-1}\right)^{\frac{1}{3}}\\= q^{ -1 . \frac{1}{3} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)