Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-2}{5} - \frac{1}{2} }= y^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ y^{9} }}=\frac{1}{\sqrt[10]{ y^{9} }}. \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y|}\\---------------\)
2. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{1}{2} - (\frac{-1}{3}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
3. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-5}{2} - \frac{5}{3} }= a^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ a^{25} }}\\=\frac{1}{|a^{4}|.\sqrt[6]{ a }}=\frac{1}{|a^{4}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{5}|}\\---------------\)
4. \(\dfrac{a^{-1}}{a^{1}}\\= a^{ -1 - 1 }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
5. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{1}{4}}}\\= x^{ \frac{5}{3} - \frac{1}{4} }= x^{\frac{17}{12}}\\=\sqrt[12]{ x^{17} }=|x|.\sqrt[12]{ x^{5} }\\---------------\)
6. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-3}{2} - (\frac{-5}{2}) }= y^{1}\\\\---------------\)
7. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{2}{5} - (\frac{-1}{6}) }= y^{\frac{17}{30}}\\=\sqrt[30]{ y^{17} }\\---------------\)
8. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{3}}}\\= x^{ \frac{1}{2} - \frac{1}{3} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
9. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{3} - \frac{1}{2} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
10. \(\dfrac{x^{2}}{x^{\frac{-2}{5}}}\\= x^{ 2 - (\frac{-2}{5}) }= x^{\frac{12}{5}}\\=\sqrt[5]{ x^{12} }=x^{2}.\sqrt[5]{ x^{2} }\\---------------\)
11. \(\dfrac{q^{1}}{q^{\frac{-2}{3}}}\\= q^{ 1 - (\frac{-2}{3}) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
12. \(\dfrac{y^{-1}}{y^{\frac{1}{3}}}\\= y^{ -1 - \frac{1}{3} }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)