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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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