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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-5}{3}}\right)^{\frac{1}{3}}\\= a^{ \frac{-5}{3} . \frac{1}{3} }= a^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ a^{5} }}=\frac{1}{\sqrt[9]{ a^{5} }}. \color{purple}{\frac{\sqrt[9]{ a^{4} }}{\sqrt[9]{ a^{4} }}} \\=\frac{\sqrt[9]{ a^{4} }}{a}\\---------------\)
2. \(\left(x^{1}\right)^{\frac{-2}{3}}\\= x^{ 1 . (\frac{-2}{3}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
3. \(\left(q^{\frac{-4}{3}}\right)^{\frac{4}{3}}\\= q^{ \frac{-4}{3} . \frac{4}{3} }= q^{\frac{-16}{9}}\\=\frac{1}{\sqrt[9]{ q^{16} }}\\=\frac{1}{q.\sqrt[9]{ q^{7} }}=\frac{1}{q.\sqrt[9]{ q^{7} }} \color{purple}{\frac{\sqrt[9]{ q^{2} }}{\sqrt[9]{ q^{2} }}} \\=\frac{\sqrt[9]{ q^{2} }}{q^{2}}\\---------------\)
4. \(\left(a^{\frac{-1}{4}}\right)^{\frac{1}{2}}\\= a^{ \frac{-1}{4} . \frac{1}{2} }= a^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ a }}=\frac{1}{\sqrt[8]{ a }}. \color{purple}{\frac{\sqrt[8]{ a^{7} }}{\sqrt[8]{ a^{7} }}} \\=\frac{\sqrt[8]{ a^{7} }}{|a|}\\---------------\)
5. \(\left(q^{\frac{4}{3}}\right)^{\frac{-4}{5}}\\= q^{ \frac{4}{3} . (\frac{-4}{5}) }= q^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ q^{16} }}\\=\frac{1}{q.\sqrt[15]{ q }}=\frac{1}{q.\sqrt[15]{ q }} \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q^{2}}\\---------------\)
6. \(\left(x^{1}\right)^{\frac{-5}{3}}\\= x^{ 1 . (\frac{-5}{3}) }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
7. \(\left(q^{\frac{-1}{5}}\right)^{\frac{3}{5}}\\= q^{ \frac{-1}{5} . \frac{3}{5} }= q^{\frac{-3}{25}}\\=\frac{1}{\sqrt[25]{ q^{3} }}=\frac{1}{\sqrt[25]{ q^{3} }}. \color{purple}{\frac{\sqrt[25]{ q^{22} }}{\sqrt[25]{ q^{22} }}} \\=\frac{\sqrt[25]{ q^{22} }}{q}\\---------------\)
8. \(\left(y^{\frac{1}{4}}\right)^{\frac{-1}{2}}\\= y^{ \frac{1}{4} . (\frac{-1}{2}) }= y^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ y }}=\frac{1}{\sqrt[8]{ y }}. \color{purple}{\frac{\sqrt[8]{ y^{7} }}{\sqrt[8]{ y^{7} }}} \\=\frac{\sqrt[8]{ y^{7} }}{|y|}\\---------------\)
9. \(\left(a^{\frac{1}{2}}\right)^{\frac{5}{6}}\\= a^{ \frac{1}{2} . \frac{5}{6} }= a^{\frac{5}{12}}\\=\sqrt[12]{ a^{5} }\\---------------\)
10. \(\left(x^{\frac{3}{4}}\right)^{\frac{5}{3}}\\= x^{ \frac{3}{4} . \frac{5}{3} }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
11. \(\left(q^{\frac{-3}{2}}\right)^{\frac{3}{2}}\\= q^{ \frac{-3}{2} . \frac{3}{2} }= q^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ q^{9} }}\\=\frac{1}{|q^{2}|.\sqrt[4]{ q }}=\frac{1}{|q^{2}|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{3}|}\\---------------\)
12. \(\left(x^{\frac{5}{2}}\right)^{\frac{-1}{2}}\\= x^{ \frac{5}{2} . (\frac{-1}{2}) }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)