Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{-1}}{q^{\frac{-2}{5}}}\\= q^{ -1 - (\frac{-2}{5}) }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
2. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{4}{5} - (\frac{-2}{5}) }= a^{\frac{6}{5}}\\=\sqrt[5]{ a^{6} }=a.\sqrt[5]{ a }\\---------------\)
3. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{3}{2}}}\\= q^{ \frac{2}{5} - \frac{3}{2} }= q^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[10]{ q }}=\frac{1}{|q|.\sqrt[10]{ q }} \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q^{2}|}\\---------------\)
4. \(\dfrac{a^{1}}{a^{\frac{-4}{3}}}\\= a^{ 1 - (\frac{-4}{3}) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
5. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{1}{5}}}\\= x^{ \frac{2}{5} - \frac{1}{5} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
6. \(\dfrac{a^{2}}{a^{-1}}\\= a^{ 2 - (-1) }= a^{3}\\\\---------------\)
7. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{4}{3}}}\\= q^{ \frac{-4}{3} - \frac{4}{3} }= q^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ q^{8} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }}=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{3}}\\---------------\)
8. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{1}{4} - (\frac{-5}{6}) }= q^{\frac{13}{12}}\\=\sqrt[12]{ q^{13} }=|q|.\sqrt[12]{ q }\\---------------\)
9. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-5}{4} - \frac{1}{2} }= y^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[4]{ y^{3} }}=\frac{1}{|y|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{2}|}\\---------------\)
10. \(\dfrac{a^{1}}{a^{\frac{1}{5}}}\\= a^{ 1 - \frac{1}{5} }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)
11. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-3}{2} - \frac{2}{3} }= a^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ a^{13} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a }}=\frac{1}{|a^{2}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{3}|}\\---------------\)
12. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{-1}{2} - (\frac{-3}{4}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)