Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{2}}}{x^{-2}}\\= x^{ \frac{-1}{2} - (-2) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
2. \(\dfrac{x^{-1}}{x^{-1}}\\= x^{ -1 - (-1) }= x^{0}\\=1\\---------------\)
3. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{-3}{4} - (\frac{-1}{6}) }= q^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ q^{7} }}=\frac{1}{\sqrt[12]{ q^{7} }}. \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q|}\\---------------\)
4. \(\dfrac{q^{-2}}{q^{\frac{-1}{5}}}\\= q^{ -2 - (\frac{-1}{5}) }= q^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ q^{9} }}\\=\frac{1}{q.\sqrt[5]{ q^{4} }}=\frac{1}{q.\sqrt[5]{ q^{4} }} \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q^{2}}\\---------------\)
5. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{1}{2}}}\\= x^{ \frac{2}{5} - \frac{1}{2} }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
6. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{1}{3} - (\frac{-1}{2}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
7. \(\dfrac{a^{-1}}{a^{\frac{-3}{4}}}\\= a^{ -1 - (\frac{-3}{4}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
8. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-4}{3} - (\frac{-1}{2}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
9. \(\dfrac{a^{1}}{a^{\frac{-3}{2}}}\\= a^{ 1 - (\frac{-3}{2}) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
10. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{-2}{5} - (\frac{-2}{5}) }= y^{0}\\=1\\---------------\)
11. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{1}{5}}}\\= x^{ \frac{-1}{3} - \frac{1}{5} }= x^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ x^{8} }}=\frac{1}{\sqrt[15]{ x^{8} }}. \color{purple}{\frac{\sqrt[15]{ x^{7} }}{\sqrt[15]{ x^{7} }}} \\=\frac{\sqrt[15]{ x^{7} }}{x}\\---------------\)
12. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-1}{2} - (\frac{-5}{3}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)