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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{1}\right)^{\frac{5}{3}}\\= q^{ 1 . \frac{5}{3} }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
2. \(\left(q^{\frac{-1}{5}}\right)^{\frac{1}{5}}\\= q^{ \frac{-1}{5} . \frac{1}{5} }= q^{\frac{-1}{25}}\\=\frac{1}{\sqrt[25]{ q }}=\frac{1}{\sqrt[25]{ q }}. \color{purple}{\frac{\sqrt[25]{ q^{24} }}{\sqrt[25]{ q^{24} }}} \\=\frac{\sqrt[25]{ q^{24} }}{q}\\---------------\)
3. \(\left(x^{1}\right)^{\frac{1}{5}}\\= x^{ 1 . \frac{1}{5} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
4. \(\left(x^{\frac{-5}{4}}\right)^{\frac{1}{3}}\\= x^{ \frac{-5}{4} . \frac{1}{3} }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
5. \(\left(y^{\frac{-1}{2}}\right)^{\frac{4}{3}}\\= y^{ \frac{-1}{2} . \frac{4}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
6. \(\left(y^{-1}\right)^{\frac{-1}{2}}\\= y^{ -1 . (\frac{-1}{2}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
7. \(\left(q^{\frac{-1}{4}}\right)^{\frac{2}{3}}\\= q^{ \frac{-1}{4} . \frac{2}{3} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
8. \(\left(x^{\frac{1}{2}}\right)^{\frac{-2}{3}}\\= x^{ \frac{1}{2} . (\frac{-2}{3}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
9. \(\left(a^{1}\right)^{\frac{-3}{5}}\\= a^{ 1 . (\frac{-3}{5}) }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
10. \(\left(a^{2}\right)^{\frac{5}{3}}\\= a^{ 2 . \frac{5}{3} }= a^{\frac{10}{3}}\\=\sqrt[3]{ a^{10} }=a^{3}.\sqrt[3]{ a }\\---------------\)
11. \(\left(y^{\frac{-1}{2}}\right)^{\frac{3}{4}}\\= y^{ \frac{-1}{2} . \frac{3}{4} }= y^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ y^{3} }}=\frac{1}{\sqrt[8]{ y^{3} }}. \color{purple}{\frac{\sqrt[8]{ y^{5} }}{\sqrt[8]{ y^{5} }}} \\=\frac{\sqrt[8]{ y^{5} }}{|y|}\\---------------\)
12. \(\left(q^{\frac{-3}{2}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-3}{2} . (\frac{-1}{2}) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)