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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{1}\right)^{\frac{3}{4}}\\= q^{ 1 . \frac{3}{4} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
2. \(\left(q^{\frac{-4}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-4}{3} . (\frac{-1}{2}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
3. \(\left(a^{\frac{2}{3}}\right)^{\frac{3}{4}}\\= a^{ \frac{2}{3} . \frac{3}{4} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
4. \(\left(q^{\frac{-4}{5}}\right)^{\frac{1}{2}}\\= q^{ \frac{-4}{5} . \frac{1}{2} }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
5. \(\left(x^{\frac{-5}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{-5}{3} . \frac{1}{2} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
6. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-1}{2} . (\frac{-1}{2}) }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
7. \(\left(y^{-1}\right)^{\frac{-1}{2}}\\= y^{ -1 . (\frac{-1}{2}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
8. \(\left(a^{\frac{1}{2}}\right)^{2}\\= a^{ \frac{1}{2} . 2 }= a^{1}\\\\---------------\)
9. \(\left(q^{\frac{-5}{6}}\right)^{\frac{1}{2}}\\= q^{ \frac{-5}{6} . \frac{1}{2} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
10. \(\left(q^{\frac{2}{3}}\right)^{\frac{-3}{5}}\\= q^{ \frac{2}{3} . (\frac{-3}{5}) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
11. \(\left(y^{\frac{-3}{5}}\right)^{\frac{4}{5}}\\= y^{ \frac{-3}{5} . \frac{4}{5} }= y^{\frac{-12}{25}}\\=\frac{1}{\sqrt[25]{ y^{12} }}=\frac{1}{\sqrt[25]{ y^{12} }}. \color{purple}{\frac{\sqrt[25]{ y^{13} }}{\sqrt[25]{ y^{13} }}} \\=\frac{\sqrt[25]{ y^{13} }}{y}\\---------------\)
12. \(\left(y^{\frac{-5}{4}}\right)^{-1}\\= y^{ \frac{-5}{4} . (-1) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)