Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{-1}}{x^{\frac{-1}{3}}}\\= x^{ -1 - (\frac{-1}{3}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
2. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-1}{5} - \frac{5}{4} }= x^{\frac{-29}{20}}\\=\frac{1}{\sqrt[20]{ x^{29} }}\\=\frac{1}{|x|.\sqrt[20]{ x^{9} }}=\frac{1}{|x|.\sqrt[20]{ x^{9} }} \color{purple}{\frac{\sqrt[20]{ x^{11} }}{\sqrt[20]{ x^{11} }}} \\=\frac{\sqrt[20]{ x^{11} }}{|x^{2}|}\\---------------\)
3. \(\dfrac{x^{\frac{-2}{3}}}{x^{1}}\\= x^{ \frac{-2}{3} - 1 }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
4. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{2}{3} - \frac{1}{2} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
5. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-1}{3} - \frac{2}{3} }= x^{-1}\\=\frac{1}{x}\\---------------\)
6. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{3}{2} - (\frac{-1}{2}) }= q^{2}\\\\---------------\)
7. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{1}{3} - (\frac{-2}{3}) }= q^{1}\\\\---------------\)
8. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{2}{5} - (\frac{-5}{3}) }= q^{\frac{31}{15}}\\=\sqrt[15]{ q^{31} }=q^{2}.\sqrt[15]{ q }\\---------------\)
9. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{3}{4}}}\\= q^{ \frac{-1}{2} - \frac{3}{4} }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
10. \(\dfrac{a^{\frac{-1}{4}}}{a^{2}}\\= a^{ \frac{-1}{4} - 2 }= a^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ a^{9} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a }}=\frac{1}{|a^{2}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{3}|}\\---------------\)
11. \(\dfrac{q^{-1}}{q^{\frac{3}{5}}}\\= q^{ -1 - \frac{3}{5} }= q^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ q^{8} }}\\=\frac{1}{q.\sqrt[5]{ q^{3} }}=\frac{1}{q.\sqrt[5]{ q^{3} }} \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q^{2}}\\---------------\)
12. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{-5}{2} - (\frac{-1}{4}) }= x^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ x^{9} }}\\=\frac{1}{|x^{2}|.\sqrt[4]{ x }}=\frac{1}{|x^{2}|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{3}|}\\---------------\)