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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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