Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-1}{3} - (\frac{-1}{3}) }= q^{0}\\=1\\---------------\)
2. \(\dfrac{q^{\frac{4}{3}}}{q^{-1}}\\= q^{ \frac{4}{3} - (-1) }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
3. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{4}) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
4. \(\dfrac{q^{2}}{q^{\frac{-1}{2}}}\\= q^{ 2 - (\frac{-1}{2}) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
5. \(\dfrac{q^{-1}}{q^{\frac{-5}{2}}}\\= q^{ -1 - (\frac{-5}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
6. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{3} - (\frac{-1}{2}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
7. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{-3}{4} - (\frac{-2}{5}) }= a^{\frac{-7}{20}}\\=\frac{1}{\sqrt[20]{ a^{7} }}=\frac{1}{\sqrt[20]{ a^{7} }}. \color{purple}{\frac{\sqrt[20]{ a^{13} }}{\sqrt[20]{ a^{13} }}} \\=\frac{\sqrt[20]{ a^{13} }}{|a|}\\---------------\)
8. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{1}{4}}}\\= y^{ \frac{3}{4} - \frac{1}{4} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
9. \(\dfrac{x^{\frac{-1}{4}}}{x^{1}}\\= x^{ \frac{-1}{4} - 1 }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
10. \(\dfrac{q^{-2}}{q^{\frac{5}{2}}}\\= q^{ -2 - \frac{5}{2} }= q^{\frac{-9}{2}}\\=\frac{1}{ \sqrt{ q^{9} } }\\=\frac{1}{|q^{4}|. \sqrt{ q } }=\frac{1}{|q^{4}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{5}|}\\---------------\)
11. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-1}{2} - \frac{4}{5} }= y^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ y^{13} }}\\=\frac{1}{|y|.\sqrt[10]{ y^{3} }}=\frac{1}{|y|.\sqrt[10]{ y^{3} }} \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y^{2}|}\\---------------\)
12. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-3}{5} - (\frac{-2}{3}) }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)