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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{2}}\right)^{\frac{3}{4}}\\= y^{ \frac{1}{2} . \frac{3}{4} }= y^{\frac{3}{8}}\\=\sqrt[8]{ y^{3} }\\---------------\)
2. \(\left(a^{\frac{-3}{2}}\right)^{\frac{2}{3}}\\= a^{ \frac{-3}{2} . \frac{2}{3} }= a^{-1}\\=\frac{1}{a}\\---------------\)
3. \(\left(x^{\frac{-1}{2}}\right)^{\frac{4}{5}}\\= x^{ \frac{-1}{2} . \frac{4}{5} }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
4. \(\left(x^{\frac{-5}{6}}\right)^{\frac{1}{4}}\\= x^{ \frac{-5}{6} . \frac{1}{4} }= x^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ x^{5} }}=\frac{1}{\sqrt[24]{ x^{5} }}. \color{purple}{\frac{\sqrt[24]{ x^{19} }}{\sqrt[24]{ x^{19} }}} \\=\frac{\sqrt[24]{ x^{19} }}{|x|}\\---------------\)
5. \(\left(x^{-2}\right)^{2}\\= x^{ -2 . 2 }= x^{-4}\\=\frac{1}{x^{4}}\\---------------\)
6. \(\left(q^{\frac{-1}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-1}{3} . (\frac{-1}{2}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
7. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-1}{2} . (\frac{-1}{2}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
8. \(\left(x^{\frac{-5}{6}}\right)^{\frac{-1}{5}}\\= x^{ \frac{-5}{6} . (\frac{-1}{5}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
9. \(\left(y^{-1}\right)^{\frac{1}{2}}\\= y^{ -1 . \frac{1}{2} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
10. \(\left(y^{-1}\right)^{-1}\\= y^{ -1 . (-1) }= y^{1}\\\\---------------\)
11. \(\left(y^{1}\right)^{\frac{3}{4}}\\= y^{ 1 . \frac{3}{4} }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
12. \(\left(a^{\frac{-1}{4}}\right)^{\frac{-5}{6}}\\= a^{ \frac{-1}{4} . (\frac{-5}{6}) }= a^{\frac{5}{24}}\\=\sqrt[24]{ a^{5} }\\---------------\)