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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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