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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{3}{5}}\right)^{\frac{1}{2}}\\= x^{ \frac{3}{5} . \frac{1}{2} }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
2. \(\left(y^{-1}\right)^{\frac{-5}{4}}\\= y^{ -1 . (\frac{-5}{4}) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
3. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-2}{3}}\\= y^{ \frac{-2}{5} . (\frac{-2}{3}) }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
4. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-5}{4}}\\= q^{ \frac{-2}{3} . (\frac{-5}{4}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
5. \(\left(y^{1}\right)^{\frac{-2}{5}}\\= y^{ 1 . (\frac{-2}{5}) }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
6. \(\left(y^{\frac{-1}{5}}\right)^{2}\\= y^{ \frac{-1}{5} . 2 }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
7. \(\left(a^{\frac{-3}{5}}\right)^{\frac{-2}{5}}\\= a^{ \frac{-3}{5} . (\frac{-2}{5}) }= a^{\frac{6}{25}}\\=\sqrt[25]{ a^{6} }\\---------------\)
8. \(\left(a^{\frac{-4}{3}}\right)^{\frac{-5}{4}}\\= a^{ \frac{-4}{3} . (\frac{-5}{4}) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
9. \(\left(q^{\frac{-4}{3}}\right)^{2}\\= q^{ \frac{-4}{3} . 2 }= q^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ q^{8} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }}=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{3}}\\---------------\)
10. \(\left(a^{\frac{-1}{4}}\right)^{\frac{1}{3}}\\= a^{ \frac{-1}{4} . \frac{1}{3} }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
11. \(\left(a^{-2}\right)^{\frac{-3}{5}}\\= a^{ -2 . (\frac{-3}{5}) }= a^{\frac{6}{5}}\\=\sqrt[5]{ a^{6} }=a.\sqrt[5]{ a }\\---------------\)
12. \(\left(a^{\frac{3}{4}}\right)^{1}\\= a^{ \frac{3}{4} . 1 }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)