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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-1}{4}}\right)^{\frac{3}{2}}\\= a^{ \frac{-1}{4} . \frac{3}{2} }= a^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ a^{3} }}=\frac{1}{\sqrt[8]{ a^{3} }}. \color{purple}{\frac{\sqrt[8]{ a^{5} }}{\sqrt[8]{ a^{5} }}} \\=\frac{\sqrt[8]{ a^{5} }}{|a|}\\---------------\)
2. \(\left(a^{\frac{-2}{5}}\right)^{\frac{-3}{2}}\\= a^{ \frac{-2}{5} . (\frac{-3}{2}) }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
3. \(\left(x^{\frac{4}{3}}\right)^{\frac{5}{2}}\\= x^{ \frac{4}{3} . \frac{5}{2} }= x^{\frac{10}{3}}\\=\sqrt[3]{ x^{10} }=x^{3}.\sqrt[3]{ x }\\---------------\)
4. \(\left(x^{\frac{-5}{2}}\right)^{-2}\\= x^{ \frac{-5}{2} . (-2) }= x^{5}\\\\---------------\)
5. \(\left(y^{\frac{2}{3}}\right)^{-1}\\= y^{ \frac{2}{3} . (-1) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
6. \(\left(x^{\frac{5}{2}}\right)^{\frac{-5}{4}}\\= x^{ \frac{5}{2} . (\frac{-5}{4}) }= x^{\frac{-25}{8}}\\=\frac{1}{\sqrt[8]{ x^{25} }}\\=\frac{1}{|x^{3}|.\sqrt[8]{ x }}=\frac{1}{|x^{3}|.\sqrt[8]{ x }} \color{purple}{\frac{\sqrt[8]{ x^{7} }}{\sqrt[8]{ x^{7} }}} \\=\frac{\sqrt[8]{ x^{7} }}{|x^{4}|}\\---------------\)
7. \(\left(q^{\frac{5}{2}}\right)^{\frac{3}{4}}\\= q^{ \frac{5}{2} . \frac{3}{4} }= q^{\frac{15}{8}}\\=\sqrt[8]{ q^{15} }=|q|.\sqrt[8]{ q^{7} }\\---------------\)
8. \(\left(y^{\frac{3}{4}}\right)^{\frac{-1}{2}}\\= y^{ \frac{3}{4} . (\frac{-1}{2}) }= y^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ y^{3} }}=\frac{1}{\sqrt[8]{ y^{3} }}. \color{purple}{\frac{\sqrt[8]{ y^{5} }}{\sqrt[8]{ y^{5} }}} \\=\frac{\sqrt[8]{ y^{5} }}{|y|}\\---------------\)
9. \(\left(x^{\frac{3}{4}}\right)^{1}\\= x^{ \frac{3}{4} . 1 }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
10. \(\left(a^{\frac{2}{3}}\right)^{\frac{-5}{4}}\\= a^{ \frac{2}{3} . (\frac{-5}{4}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
11. \(\left(x^{-1}\right)^{\frac{1}{3}}\\= x^{ -1 . \frac{1}{3} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
12. \(\left(q^{1}\right)^{\frac{-2}{5}}\\= q^{ 1 . (\frac{-2}{5}) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)