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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{3}{5}}\right)^{\frac{-1}{5}}\\= x^{ \frac{3}{5} . (\frac{-1}{5}) }= x^{\frac{-3}{25}}\\=\frac{1}{\sqrt[25]{ x^{3} }}=\frac{1}{\sqrt[25]{ x^{3} }}. \color{purple}{\frac{\sqrt[25]{ x^{22} }}{\sqrt[25]{ x^{22} }}} \\=\frac{\sqrt[25]{ x^{22} }}{x}\\---------------\)
2. \(\left(a^{\frac{-3}{2}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-3}{2} . (\frac{-1}{3}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
3. \(\left(q^{\frac{3}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{3}{2} . \frac{1}{2} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
4. \(\left(q^{\frac{-4}{5}}\right)^{-2}\\= q^{ \frac{-4}{5} . (-2) }= q^{\frac{8}{5}}\\=\sqrt[5]{ q^{8} }=q.\sqrt[5]{ q^{3} }\\---------------\)
5. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-2}{3}}\\= y^{ \frac{-1}{2} . (\frac{-2}{3}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
6. \(\left(y^{1}\right)^{\frac{1}{2}}\\= y^{ 1 . \frac{1}{2} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
7. \(\left(x^{\frac{5}{2}}\right)^{\frac{-2}{3}}\\= x^{ \frac{5}{2} . (\frac{-2}{3}) }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
8. \(\left(x^{\frac{-5}{2}}\right)^{-1}\\= x^{ \frac{-5}{2} . (-1) }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
9. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-2}{5}}\\= x^{ \frac{-1}{3} . (\frac{-2}{5}) }= x^{\frac{2}{15}}\\=\sqrt[15]{ x^{2} }\\---------------\)
10. \(\left(q^{1}\right)^{1}\\= q^{ 1 . 1 }= q^{1}\\\\---------------\)
11. \(\left(x^{\frac{3}{4}}\right)^{\frac{5}{6}}\\= x^{ \frac{3}{4} . \frac{5}{6} }= x^{\frac{5}{8}}\\=\sqrt[8]{ x^{5} }\\---------------\)
12. \(\left(a^{1}\right)^{\frac{-3}{2}}\\= a^{ 1 . (\frac{-3}{2}) }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)