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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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