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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{1}{2} . \frac{1}{2} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
2. \(\left(y^{1}\right)^{\frac{-5}{3}}\\= y^{ 1 . (\frac{-5}{3}) }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
3. \(\left(q^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{-1}{2} . \frac{1}{2} }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
4. \(\left(y^{-2}\right)^{\frac{1}{4}}\\= y^{ -2 . \frac{1}{4} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
5. \(\left(a^{\frac{5}{2}}\right)^{\frac{-5}{3}}\\= a^{ \frac{5}{2} . (\frac{-5}{3}) }= a^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ a^{25} }}\\=\frac{1}{|a^{4}|.\sqrt[6]{ a }}=\frac{1}{|a^{4}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{5}|}\\---------------\)
6. \(\left(y^{\frac{-1}{4}}\right)^{\frac{-5}{6}}\\= y^{ \frac{-1}{4} . (\frac{-5}{6}) }= y^{\frac{5}{24}}\\=\sqrt[24]{ y^{5} }\\---------------\)
7. \(\left(q^{\frac{1}{4}}\right)^{\frac{-1}{3}}\\= q^{ \frac{1}{4} . (\frac{-1}{3}) }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
8. \(\left(x^{\frac{1}{3}}\right)^{\frac{-2}{3}}\\= x^{ \frac{1}{3} . (\frac{-2}{3}) }= x^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ x^{2} }}=\frac{1}{\sqrt[9]{ x^{2} }}. \color{purple}{\frac{\sqrt[9]{ x^{7} }}{\sqrt[9]{ x^{7} }}} \\=\frac{\sqrt[9]{ x^{7} }}{x}\\---------------\)
9. \(\left(a^{\frac{-3}{5}}\right)^{\frac{3}{4}}\\= a^{ \frac{-3}{5} . \frac{3}{4} }= a^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ a^{9} }}=\frac{1}{\sqrt[20]{ a^{9} }}. \color{purple}{\frac{\sqrt[20]{ a^{11} }}{\sqrt[20]{ a^{11} }}} \\=\frac{\sqrt[20]{ a^{11} }}{|a|}\\---------------\)
10. \(\left(x^{1}\right)^{\frac{-4}{5}}\\= x^{ 1 . (\frac{-4}{5}) }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)
11. \(\left(x^{-1}\right)^{\frac{2}{3}}\\= x^{ -1 . \frac{2}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
12. \(\left(a^{\frac{-2}{3}}\right)^{\frac{4}{3}}\\= a^{ \frac{-2}{3} . \frac{4}{3} }= a^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ a^{8} }}=\frac{1}{\sqrt[9]{ a^{8} }}. \color{purple}{\frac{\sqrt[9]{ a }}{\sqrt[9]{ a }}} \\=\frac{\sqrt[9]{ a }}{a}\\---------------\)