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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{2}}\right)^{-2}\\= y^{ \frac{1}{2} . (-2) }= y^{-1}\\=\frac{1}{y}\\---------------\)
2. \(\left(y^{\frac{5}{2}}\right)^{\frac{5}{3}}\\= y^{ \frac{5}{2} . \frac{5}{3} }= y^{\frac{25}{6}}\\=\sqrt[6]{ y^{25} }=|y^{4}|.\sqrt[6]{ y }\\---------------\)
3. \(\left(y^{\frac{-5}{4}}\right)^{\frac{-1}{4}}\\= y^{ \frac{-5}{4} . (\frac{-1}{4}) }= y^{\frac{5}{16}}\\=\sqrt[16]{ y^{5} }\\---------------\)
4. \(\left(y^{\frac{1}{4}}\right)^{\frac{5}{3}}\\= y^{ \frac{1}{4} . \frac{5}{3} }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
5. \(\left(x^{1}\right)^{1}\\= x^{ 1 . 1 }= x^{1}\\\\---------------\)
6. \(\left(y^{\frac{3}{5}}\right)^{\frac{3}{2}}\\= y^{ \frac{3}{5} . \frac{3}{2} }= y^{\frac{9}{10}}\\=\sqrt[10]{ y^{9} }\\---------------\)
7. \(\left(a^{\frac{3}{5}}\right)^{\frac{-5}{4}}\\= a^{ \frac{3}{5} . (\frac{-5}{4}) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
8. \(\left(q^{\frac{1}{4}}\right)^{\frac{-1}{5}}\\= q^{ \frac{1}{4} . (\frac{-1}{5}) }= q^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ q }}=\frac{1}{\sqrt[20]{ q }}. \color{purple}{\frac{\sqrt[20]{ q^{19} }}{\sqrt[20]{ q^{19} }}} \\=\frac{\sqrt[20]{ q^{19} }}{|q|}\\---------------\)
9. \(\left(q^{\frac{-4}{3}}\right)^{1}\\= q^{ \frac{-4}{3} . 1 }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
10. \(\left(x^{\frac{1}{2}}\right)^{2}\\= x^{ \frac{1}{2} . 2 }= x^{1}\\\\---------------\)
11. \(\left(q^{1}\right)^{\frac{-1}{3}}\\= q^{ 1 . (\frac{-1}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
12. \(\left(q^{-1}\right)^{1}\\= q^{ -1 . 1 }= q^{-1}\\=\frac{1}{q}\\---------------\)