Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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