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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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