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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{5}{2}}\right)^{\frac{-3}{4}}\\= a^{ \frac{5}{2} . (\frac{-3}{4}) }= a^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ a^{15} }}\\=\frac{1}{|a|.\sqrt[8]{ a^{7} }}=\frac{1}{|a|.\sqrt[8]{ a^{7} }} \color{purple}{\frac{\sqrt[8]{ a }}{\sqrt[8]{ a }}} \\=\frac{\sqrt[8]{ a }}{|a^{2}|}\\---------------\)
2. \(\left(a^{\frac{-1}{4}}\right)^{\frac{-1}{6}}\\= a^{ \frac{-1}{4} . (\frac{-1}{6}) }= a^{\frac{1}{24}}\\=\sqrt[24]{ a }\\---------------\)
3. \(\left(q^{\frac{-3}{2}}\right)^{\frac{-3}{4}}\\= q^{ \frac{-3}{2} . (\frac{-3}{4}) }= q^{\frac{9}{8}}\\=\sqrt[8]{ q^{9} }=|q|.\sqrt[8]{ q }\\---------------\)
4. \(\left(q^{\frac{4}{5}}\right)^{\frac{5}{3}}\\= q^{ \frac{4}{5} . \frac{5}{3} }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
5. \(\left(q^{\frac{-3}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{-3}{2} . \frac{1}{2} }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
6. \(\left(y^{1}\right)^{\frac{2}{3}}\\= y^{ 1 . \frac{2}{3} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
7. \(\left(y^{\frac{3}{5}}\right)^{\frac{-2}{3}}\\= y^{ \frac{3}{5} . (\frac{-2}{3}) }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
8. \(\left(y^{\frac{1}{2}}\right)^{\frac{2}{3}}\\= y^{ \frac{1}{2} . \frac{2}{3} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
9. \(\left(q^{\frac{-4}{3}}\right)^{2}\\= q^{ \frac{-4}{3} . 2 }= q^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ q^{8} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }}=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{3}}\\---------------\)
10. \(\left(q^{-2}\right)^{\frac{3}{5}}\\= q^{ -2 . \frac{3}{5} }= q^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ q^{6} }}\\=\frac{1}{q.\sqrt[5]{ q }}=\frac{1}{q.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{2}}\\---------------\)
11. \(\left(x^{\frac{-5}{3}}\right)^{\frac{-3}{4}}\\= x^{ \frac{-5}{3} . (\frac{-3}{4}) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
12. \(\left(q^{\frac{1}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{1}{2} . \frac{1}{2} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)