Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-1}{3} - \frac{1}{2} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
2. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-1}{3} - \frac{2}{3} }= x^{-1}\\=\frac{1}{x}\\---------------\)
3. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{-1}{3} - (\frac{-1}{6}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
4. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{2}{5}}}\\= a^{ \frac{2}{3} - \frac{2}{5} }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
5. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{3}{4}}}\\= a^{ \frac{1}{3} - \frac{3}{4} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
6. \(\dfrac{q^{\frac{-4}{5}}}{q^{2}}\\= q^{ \frac{-4}{5} - 2 }= q^{\frac{-14}{5}}\\=\frac{1}{\sqrt[5]{ q^{14} }}\\=\frac{1}{q^{2}.\sqrt[5]{ q^{4} }}=\frac{1}{q^{2}.\sqrt[5]{ q^{4} }} \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q^{3}}\\---------------\)
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. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-1}{5} - (\frac{-1}{2}) }= a^{\frac{3}{10}}\\=\sqrt[10]{ a^{3} }\\---------------\)
9. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{1}{2} - (\frac{-2}{3}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
10. \(\dfrac{x^{\frac{2}{5}}}{x^{1}}\\= x^{ \frac{2}{5} - 1 }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)
11. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{5}{2} - (\frac{-4}{5}) }= y^{\frac{33}{10}}\\=\sqrt[10]{ y^{33} }=|y^{3}|.\sqrt[10]{ y^{3} }\\---------------\)
12. \(\dfrac{a^{-1}}{a^{\frac{-3}{4}}}\\= a^{ -1 - (\frac{-3}{4}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)