Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-1}{4} - \frac{2}{3} }= a^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ a^{11} }}=\frac{1}{\sqrt[12]{ a^{11} }}. \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a|}\\---------------\)
2. \(\dfrac{a^{\frac{1}{2}}}{a^{-1}}\\= a^{ \frac{1}{2} - (-1) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
3. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{-4}{5} - (\frac{-4}{5}) }= a^{0}\\=1\\---------------\)
4. \(\dfrac{y^{-1}}{y^{\frac{5}{3}}}\\= y^{ -1 - \frac{5}{3} }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
5. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{4}{5}}}\\= q^{ \frac{1}{2} - \frac{4}{5} }= q^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ q^{3} }}=\frac{1}{\sqrt[10]{ q^{3} }}. \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q|}\\---------------\)
6. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{3}{4}}}\\= y^{ \frac{-4}{5} - \frac{3}{4} }= y^{\frac{-31}{20}}\\=\frac{1}{\sqrt[20]{ y^{31} }}\\=\frac{1}{|y|.\sqrt[20]{ y^{11} }}=\frac{1}{|y|.\sqrt[20]{ y^{11} }} \color{purple}{\frac{\sqrt[20]{ y^{9} }}{\sqrt[20]{ y^{9} }}} \\=\frac{\sqrt[20]{ y^{9} }}{|y^{2}|}\\---------------\)
7. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-4}{5} - (\frac{-1}{2}) }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
8. \(\dfrac{y^{-1}}{y^{\frac{4}{5}}}\\= y^{ -1 - \frac{4}{5} }= y^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ y^{9} }}\\=\frac{1}{y.\sqrt[5]{ y^{4} }}=\frac{1}{y.\sqrt[5]{ y^{4} }} \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y^{2}}\\---------------\)
9. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{5}{2}}}\\= a^{ \frac{-3}{4} - \frac{5}{2} }= a^{\frac{-13}{4}}\\=\frac{1}{\sqrt[4]{ a^{13} }}\\=\frac{1}{|a^{3}|.\sqrt[4]{ a }}=\frac{1}{|a^{3}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{4}|}\\---------------\)
10. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{5}{6} - (\frac{-1}{5}) }= y^{\frac{31}{30}}\\=\sqrt[30]{ y^{31} }=|y|.\sqrt[30]{ y }\\---------------\)
11. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{5}) }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)
12. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-2}{3} - (\frac{-1}{2}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)