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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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