Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{2} - (\frac{-1}{2}) }= x^{0}\\=1\\---------------\)
2. \(\dfrac{a^{-1}}{a^{\frac{-4}{5}}}\\= a^{ -1 - (\frac{-4}{5}) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
3. \(\dfrac{q^{\frac{1}{5}}}{q^{1}}\\= q^{ \frac{1}{5} - 1 }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)
4. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{2}{3} - \frac{2}{3} }= a^{0}\\=1\\---------------\)
5. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-5}{2} - \frac{2}{5} }= x^{\frac{-29}{10}}\\=\frac{1}{\sqrt[10]{ x^{29} }}\\=\frac{1}{|x^{2}|.\sqrt[10]{ x^{9} }}=\frac{1}{|x^{2}|.\sqrt[10]{ x^{9} }} \color{purple}{\frac{\sqrt[10]{ x }}{\sqrt[10]{ x }}} \\=\frac{\sqrt[10]{ x }}{|x^{3}|}\\---------------\)
6. \(\dfrac{y^{1}}{y^{\frac{1}{5}}}\\= y^{ 1 - \frac{1}{5} }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
7. \(\dfrac{a^{1}}{a^{\frac{-1}{3}}}\\= a^{ 1 - (\frac{-1}{3}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
8. \(\dfrac{a^{-1}}{a^{\frac{2}{5}}}\\= a^{ -1 - \frac{2}{5} }= a^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ a^{7} }}\\=\frac{1}{a.\sqrt[5]{ a^{2} }}=\frac{1}{a.\sqrt[5]{ a^{2} }} \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a^{2}}\\---------------\)
9. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-4}{3} - (\frac{-1}{2}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
10. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{5}{6}}}\\= a^{ \frac{2}{3} - \frac{5}{6} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
11. \(\dfrac{y^{\frac{2}{3}}}{y^{-1}}\\= y^{ \frac{2}{3} - (-1) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
12. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{5}{2}}}\\= q^{ \frac{4}{3} - \frac{5}{2} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)