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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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