Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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