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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{4}{5}}\right)^{\frac{5}{3}}\\= y^{ \frac{4}{5} . \frac{5}{3} }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
2. \(\left(x^{\frac{1}{2}}\right)^{\frac{1}{2}}\\= x^{ \frac{1}{2} . \frac{1}{2} }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
3. \(\left(a^{\frac{1}{6}}\right)^{\frac{-1}{2}}\\= a^{ \frac{1}{6} . (\frac{-1}{2}) }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
4. \(\left(x^{\frac{-1}{3}}\right)^{-1}\\= x^{ \frac{-1}{3} . (-1) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
5. \(\left(y^{\frac{-1}{3}}\right)^{\frac{-1}{5}}\\= y^{ \frac{-1}{3} . (\frac{-1}{5}) }= y^{\frac{1}{15}}\\=\sqrt[15]{ y }\\---------------\)
6. \(\left(a^{1}\right)^{\frac{5}{3}}\\= a^{ 1 . \frac{5}{3} }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
7. \(\left(x^{\frac{4}{3}}\right)^{-1}\\= x^{ \frac{4}{3} . (-1) }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
8. \(\left(y^{\frac{-3}{2}}\right)^{\frac{3}{5}}\\= y^{ \frac{-3}{2} . \frac{3}{5} }= y^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ y^{9} }}=\frac{1}{\sqrt[10]{ y^{9} }}. \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y|}\\---------------\)
9. \(\left(a^{\frac{1}{3}}\right)^{\frac{-1}{5}}\\= a^{ \frac{1}{3} . (\frac{-1}{5}) }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)
10. \(\left(a^{\frac{3}{5}}\right)^{\frac{5}{4}}\\= a^{ \frac{3}{5} . \frac{5}{4} }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
11. \(\left(q^{\frac{-4}{3}}\right)^{1}\\= q^{ \frac{-4}{3} . 1 }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
12. \(\left(y^{\frac{1}{3}}\right)^{\frac{-4}{5}}\\= y^{ \frac{1}{3} . (\frac{-4}{5}) }= y^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ y^{4} }}=\frac{1}{\sqrt[15]{ y^{4} }}. \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y}\\---------------\)