Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{3}{2}}}\\= y^{ \frac{-3}{4} - \frac{3}{2} }= y^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ y^{9} }}\\=\frac{1}{|y^{2}|.\sqrt[4]{ y }}=\frac{1}{|y^{2}|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{3}|}\\---------------\)
2. \(\dfrac{a^{1}}{a^{\frac{-1}{3}}}\\= a^{ 1 - (\frac{-1}{3}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
3. \(\dfrac{q^{-1}}{q^{\frac{1}{2}}}\\= q^{ -1 - \frac{1}{2} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
4. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{4}{5}}}\\= q^{ \frac{-3}{2} - \frac{4}{5} }= q^{\frac{-23}{10}}\\=\frac{1}{\sqrt[10]{ q^{23} }}\\=\frac{1}{|q^{2}|.\sqrt[10]{ q^{3} }}=\frac{1}{|q^{2}|.\sqrt[10]{ q^{3} }} \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q^{3}|}\\---------------\)
5. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{3} - (\frac{-1}{2}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
6. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{2}{5}}}\\= x^{ \frac{1}{2} - \frac{2}{5} }= x^{\frac{1}{10}}\\=\sqrt[10]{ x }\\---------------\)
7. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{5}}}\\= y^{ \frac{-1}{2} - \frac{1}{5} }= y^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ y^{7} }}=\frac{1}{\sqrt[10]{ y^{7} }}. \color{purple}{\frac{\sqrt[10]{ y^{3} }}{\sqrt[10]{ y^{3} }}} \\=\frac{\sqrt[10]{ y^{3} }}{|y|}\\---------------\)
8. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{3}{4}}}\\= y^{ \frac{5}{4} - \frac{3}{4} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
9. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{4}{3} - \frac{2}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
10. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-1}{5} - \frac{1}{2} }= x^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ x^{7} }}=\frac{1}{\sqrt[10]{ x^{7} }}. \color{purple}{\frac{\sqrt[10]{ x^{3} }}{\sqrt[10]{ x^{3} }}} \\=\frac{\sqrt[10]{ x^{3} }}{|x|}\\---------------\)
11. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{-1}{2} - (\frac{-1}{5}) }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
12. \(\dfrac{a^{\frac{5}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{5}{2} - \frac{1}{3} }= a^{\frac{13}{6}}\\=\sqrt[6]{ a^{13} }=|a^{2}|.\sqrt[6]{ a }\\---------------\)