Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{1}}{a^{\frac{3}{2}}}\\= a^{ 1 - \frac{3}{2} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
2. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{3}{4}}}\\= q^{ \frac{-2}{3} - \frac{3}{4} }= q^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ q^{17} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{5} }}=\frac{1}{|q|.\sqrt[12]{ q^{5} }} \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q^{2}|}\\---------------\)
3. \(\dfrac{q^{-1}}{q^{-1}}\\= q^{ -1 - (-1) }= q^{0}\\=1\\---------------\)
4. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{5}{2}}}\\= x^{ \frac{2}{3} - \frac{5}{2} }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
5. \(\dfrac{a^{\frac{-3}{2}}}{a^{1}}\\= a^{ \frac{-3}{2} - 1 }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
6. \(\dfrac{x^{\frac{-5}{2}}}{x^{1}}\\= x^{ \frac{-5}{2} - 1 }= x^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ x^{7} } }\\=\frac{1}{|x^{3}|. \sqrt{ x } }=\frac{1}{|x^{3}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{4}|}\\---------------\)
7. \(\dfrac{y^{1}}{y^{\frac{-2}{3}}}\\= y^{ 1 - (\frac{-2}{3}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
8. \(\dfrac{y^{-1}}{y^{\frac{5}{2}}}\\= y^{ -1 - \frac{5}{2} }= y^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ y^{7} } }\\=\frac{1}{|y^{3}|. \sqrt{ y } }=\frac{1}{|y^{3}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{4}|}\\---------------\)
9. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-1}{2} - (\frac{-1}{3}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
10. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{5}{4} - (\frac{-2}{5}) }= x^{\frac{33}{20}}\\=\sqrt[20]{ x^{33} }=|x|.\sqrt[20]{ x^{13} }\\---------------\)
11. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{5}{4} - (\frac{-2}{3}) }= a^{\frac{23}{12}}\\=\sqrt[12]{ a^{23} }=|a|.\sqrt[12]{ a^{11} }\\---------------\)
12. \(\dfrac{a^{1}}{a^{\frac{1}{2}}}\\= a^{ 1 - \frac{1}{2} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)