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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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