Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{1}}{x^{1}}\\= x^{ 1 - 1 }= x^{0}\\=1\\---------------\)
2. \(\dfrac{a^{\frac{3}{2}}}{a^{-1}}\\= a^{ \frac{3}{2} - (-1) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
3. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{4}{3} - \frac{1}{2} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
4. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{5}{3} - (\frac{-3}{5}) }= q^{\frac{34}{15}}\\=\sqrt[15]{ q^{34} }=q^{2}.\sqrt[15]{ q^{4} }\\---------------\)
5. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{3}{5}}}\\= q^{ \frac{3}{2} - \frac{3}{5} }= q^{\frac{9}{10}}\\=\sqrt[10]{ q^{9} }\\---------------\)
6. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{1}{2} - (\frac{-4}{3}) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
7. \(\dfrac{x^{\frac{-1}{2}}}{x^{1}}\\= x^{ \frac{-1}{2} - 1 }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
8. \(\dfrac{a^{-1}}{a^{\frac{-3}{4}}}\\= a^{ -1 - (\frac{-3}{4}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
9. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{1}{2}}}\\= a^{ \frac{4}{5} - \frac{1}{2} }= a^{\frac{3}{10}}\\=\sqrt[10]{ a^{3} }\\---------------\)
10. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{3} - \frac{1}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
11. \(\dfrac{y^{\frac{1}{2}}}{y^{-2}}\\= y^{ \frac{1}{2} - (-2) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
12. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{-5}{4} - (\frac{-3}{5}) }= a^{\frac{-13}{20}}\\=\frac{1}{\sqrt[20]{ a^{13} }}=\frac{1}{\sqrt[20]{ a^{13} }}. \color{purple}{\frac{\sqrt[20]{ a^{7} }}{\sqrt[20]{ a^{7} }}} \\=\frac{\sqrt[20]{ a^{7} }}{|a|}\\---------------\)