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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{5}{4}}\right)^{\frac{-3}{5}}\\= x^{ \frac{5}{4} . (\frac{-3}{5}) }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
2. \(\left(x^{1}\right)^{\frac{1}{2}}\\= x^{ 1 . \frac{1}{2} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
3. \(\left(x^{\frac{-4}{3}}\right)^{\frac{-1}{4}}\\= x^{ \frac{-4}{3} . (\frac{-1}{4}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
4. \(\left(q^{\frac{5}{2}}\right)^{\frac{-2}{3}}\\= q^{ \frac{5}{2} . (\frac{-2}{3}) }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
5. \(\left(q^{\frac{-1}{2}}\right)^{2}\\= q^{ \frac{-1}{2} . 2 }= q^{-1}\\=\frac{1}{q}\\---------------\)
6. \(\left(x^{-1}\right)^{\frac{4}{3}}\\= x^{ -1 . \frac{4}{3} }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
7. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-4}{3}}\\= x^{ \frac{-1}{2} . (\frac{-4}{3}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
8. \(\left(q^{\frac{-5}{3}}\right)^{\frac{-1}{6}}\\= q^{ \frac{-5}{3} . (\frac{-1}{6}) }= q^{\frac{5}{18}}\\=\sqrt[18]{ q^{5} }\\---------------\)
9. \(\left(q^{\frac{5}{3}}\right)^{\frac{1}{5}}\\= q^{ \frac{5}{3} . \frac{1}{5} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
10. \(\left(a^{\frac{-2}{5}}\right)^{2}\\= a^{ \frac{-2}{5} . 2 }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)
11. \(\left(q^{\frac{4}{5}}\right)^{\frac{3}{5}}\\= q^{ \frac{4}{5} . \frac{3}{5} }= q^{\frac{12}{25}}\\=\sqrt[25]{ q^{12} }\\---------------\)
12. \(\left(y^{\frac{-4}{5}}\right)^{\frac{1}{3}}\\= y^{ \frac{-4}{5} . \frac{1}{3} }= y^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ y^{4} }}=\frac{1}{\sqrt[15]{ y^{4} }}. \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y}\\---------------\)