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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-4}{3}}\right)^{\frac{-3}{4}}\\= y^{ \frac{-4}{3} . (\frac{-3}{4}) }= y^{1}\\\\---------------\)
2. \(\left(a^{\frac{-4}{3}}\right)^{\frac{2}{3}}\\= a^{ \frac{-4}{3} . \frac{2}{3} }= a^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ a^{8} }}=\frac{1}{\sqrt[9]{ a^{8} }}. \color{purple}{\frac{\sqrt[9]{ a }}{\sqrt[9]{ a }}} \\=\frac{\sqrt[9]{ a }}{a}\\---------------\)
3. \(\left(q^{2}\right)^{-1}\\= q^{ 2 . (-1) }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
4. \(\left(x^{\frac{5}{2}}\right)^{\frac{-3}{2}}\\= x^{ \frac{5}{2} . (\frac{-3}{2}) }= x^{\frac{-15}{4}}\\=\frac{1}{\sqrt[4]{ x^{15} }}\\=\frac{1}{|x^{3}|.\sqrt[4]{ x^{3} }}=\frac{1}{|x^{3}|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{4}|}\\---------------\)
5. \(\left(a^{\frac{5}{2}}\right)^{1}\\= a^{ \frac{5}{2} . 1 }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
6. \(\left(q^{\frac{-1}{2}}\right)^{-2}\\= q^{ \frac{-1}{2} . (-2) }= q^{1}\\\\---------------\)
7. \(\left(x^{\frac{1}{5}}\right)^{\frac{4}{3}}\\= x^{ \frac{1}{5} . \frac{4}{3} }= x^{\frac{4}{15}}\\=\sqrt[15]{ x^{4} }\\---------------\)
8. \(\left(q^{1}\right)^{\frac{3}{4}}\\= q^{ 1 . \frac{3}{4} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
9. \(\left(x^{\frac{-1}{5}}\right)^{\frac{-1}{5}}\\= x^{ \frac{-1}{5} . (\frac{-1}{5}) }= x^{\frac{1}{25}}\\=\sqrt[25]{ x }\\---------------\)
10. \(\left(q^{\frac{1}{2}}\right)^{\frac{5}{6}}\\= q^{ \frac{1}{2} . \frac{5}{6} }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
11. \(\left(a^{-2}\right)^{\frac{-5}{2}}\\= a^{ -2 . (\frac{-5}{2}) }= a^{5}\\\\---------------\)
12. \(\left(a^{\frac{4}{5}}\right)^{\frac{4}{5}}\\= a^{ \frac{4}{5} . \frac{4}{5} }= a^{\frac{16}{25}}\\=\sqrt[25]{ a^{16} }\\---------------\)