Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-5}{3} - \frac{1}{2} }= x^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ x^{13} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x }}=\frac{1}{|x^{2}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{3}|}\\---------------\)
2. \(\dfrac{x^{-1}}{x^{\frac{-5}{4}}}\\= x^{ -1 - (\frac{-5}{4}) }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
3. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-1}{3} - \frac{5}{3} }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
4. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-5}{6} - \frac{5}{3} }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
5. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{3}{4}}}\\= x^{ \frac{-4}{5} - \frac{3}{4} }= x^{\frac{-31}{20}}\\=\frac{1}{\sqrt[20]{ x^{31} }}\\=\frac{1}{|x|.\sqrt[20]{ x^{11} }}=\frac{1}{|x|.\sqrt[20]{ x^{11} }} \color{purple}{\frac{\sqrt[20]{ x^{9} }}{\sqrt[20]{ x^{9} }}} \\=\frac{\sqrt[20]{ x^{9} }}{|x^{2}|}\\---------------\)
6. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{-1}{3} - (\frac{-2}{5}) }= x^{\frac{1}{15}}\\=\sqrt[15]{ x }\\---------------\)
7. \(\dfrac{a^{\frac{-1}{2}}}{a^{1}}\\= a^{ \frac{-1}{2} - 1 }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
8. \(\dfrac{q^{\frac{-3}{5}}}{q^{1}}\\= q^{ \frac{-3}{5} - 1 }= q^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ q^{8} }}\\=\frac{1}{q.\sqrt[5]{ q^{3} }}=\frac{1}{q.\sqrt[5]{ q^{3} }} \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q^{2}}\\---------------\)
9. \(\dfrac{q^{2}}{q^{\frac{-1}{2}}}\\= q^{ 2 - (\frac{-1}{2}) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
10. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{4}{3}}}\\= q^{ \frac{-5}{2} - \frac{4}{3} }= q^{\frac{-23}{6}}\\=\frac{1}{\sqrt[6]{ q^{23} }}\\=\frac{1}{|q^{3}|.\sqrt[6]{ q^{5} }}=\frac{1}{|q^{3}|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{4}|}\\---------------\)
11. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{3}{4}}}\\= x^{ \frac{2}{3} - \frac{3}{4} }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)
12. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{4}{5}}}\\= y^{ \frac{1}{2} - \frac{4}{5} }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)