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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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