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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-4}{3}}\right)^{\frac{-5}{2}}\\= x^{ \frac{-4}{3} . (\frac{-5}{2}) }= x^{\frac{10}{3}}\\=\sqrt[3]{ x^{10} }=x^{3}.\sqrt[3]{ x }\\---------------\)
2. \(\left(a^{\frac{1}{6}}\right)^{-1}\\= a^{ \frac{1}{6} . (-1) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
3. \(\left(q^{\frac{1}{2}}\right)^{2}\\= q^{ \frac{1}{2} . 2 }= q^{1}\\\\---------------\)
4. \(\left(a^{\frac{5}{2}}\right)^{\frac{-3}{4}}\\= a^{ \frac{5}{2} . (\frac{-3}{4}) }= a^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ a^{15} }}\\=\frac{1}{|a|.\sqrt[8]{ a^{7} }}=\frac{1}{|a|.\sqrt[8]{ a^{7} }} \color{purple}{\frac{\sqrt[8]{ a }}{\sqrt[8]{ a }}} \\=\frac{\sqrt[8]{ a }}{|a^{2}|}\\---------------\)
5. \(\left(x^{\frac{-1}{2}}\right)^{\frac{3}{2}}\\= x^{ \frac{-1}{2} . \frac{3}{2} }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
6. \(\left(x^{\frac{-1}{3}}\right)^{2}\\= x^{ \frac{-1}{3} . 2 }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
7. \(\left(a^{\frac{3}{4}}\right)^{-1}\\= a^{ \frac{3}{4} . (-1) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
8. \(\left(a^{\frac{-5}{4}}\right)^{\frac{-5}{6}}\\= a^{ \frac{-5}{4} . (\frac{-5}{6}) }= a^{\frac{25}{24}}\\=\sqrt[24]{ a^{25} }=|a|.\sqrt[24]{ a }\\---------------\)
9. \(\left(a^{\frac{-1}{2}}\right)^{1}\\= a^{ \frac{-1}{2} . 1 }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
10. \(\left(q^{\frac{-3}{4}}\right)^{\frac{4}{3}}\\= q^{ \frac{-3}{4} . \frac{4}{3} }= q^{-1}\\=\frac{1}{q}\\---------------\)
11. \(\left(y^{\frac{-3}{5}}\right)^{\frac{1}{2}}\\= y^{ \frac{-3}{5} . \frac{1}{2} }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)
12. \(\left(a^{\frac{-1}{2}}\right)^{\frac{3}{5}}\\= a^{ \frac{-1}{2} . \frac{3}{5} }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)