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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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