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Werk uit m.b.v. de rekenregels

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

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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. \(\left(q^{\frac{1}{5}}\right)^{1}\\= q^{ \frac{1}{5} . 1 }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
3. \(\left(x^{\frac{1}{2}}\right)^{\frac{-1}{2}}\\= x^{ \frac{1}{2} . (\frac{-1}{2}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
4. \(\left(a^{1}\right)^{\frac{-1}{2}}\\= a^{ 1 . (\frac{-1}{2}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
5. \(\left(a^{\frac{3}{4}}\right)^{\frac{-3}{2}}\\= a^{ \frac{3}{4} . (\frac{-3}{2}) }= a^{\frac{-9}{8}}\\=\frac{1}{\sqrt[8]{ a^{9} }}\\=\frac{1}{|a|.\sqrt[8]{ a }}=\frac{1}{|a|.\sqrt[8]{ a }} \color{purple}{\frac{\sqrt[8]{ a^{7} }}{\sqrt[8]{ a^{7} }}} \\=\frac{\sqrt[8]{ a^{7} }}{|a^{2}|}\\---------------\)
6. \(\left(a^{\frac{-1}{2}}\right)^{\frac{3}{5}}\\= a^{ \frac{-1}{2} . \frac{3}{5} }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
7. \(\left(y^{-1}\right)^{\frac{-1}{2}}\\= y^{ -1 . (\frac{-1}{2}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
8. \(\left(q^{1}\right)^{1}\\= q^{ 1 . 1 }= q^{1}\\\\---------------\)
9. \(\left(q^{\frac{-1}{4}}\right)^{\frac{5}{3}}\\= q^{ \frac{-1}{4} . \frac{5}{3} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
10. \(\left(x^{\frac{1}{3}}\right)^{-1}\\= x^{ \frac{1}{3} . (-1) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
11. \(\left(a^{\frac{3}{2}}\right)^{\frac{1}{3}}\\= a^{ \frac{3}{2} . \frac{1}{3} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
12. \(\left(a^{\frac{3}{4}}\right)^{\frac{-5}{4}}\\= a^{ \frac{3}{4} . (\frac{-5}{4}) }= a^{\frac{-15}{16}}\\=\frac{1}{\sqrt[16]{ a^{15} }}=\frac{1}{\sqrt[16]{ a^{15} }}. \color{purple}{\frac{\sqrt[16]{ a }}{\sqrt[16]{ a }}} \\=\frac{\sqrt[16]{ a }}{|a|}\\---------------\)