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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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