Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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