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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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