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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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