Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{-1}}{y^{\frac{3}{4}}}\\= y^{ -1 - \frac{3}{4} }= y^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[4]{ y^{3} }}=\frac{1}{|y|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{2}|}\\---------------\)
2. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{5}{2}}}\\= x^{ \frac{-2}{3} - \frac{5}{2} }= x^{\frac{-19}{6}}\\=\frac{1}{\sqrt[6]{ x^{19} }}\\=\frac{1}{|x^{3}|.\sqrt[6]{ x }}=\frac{1}{|x^{3}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{4}|}\\---------------\)
3. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{-1}{2} - (\frac{-2}{5}) }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
4. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-3}{5} - \frac{2}{5} }= a^{-1}\\=\frac{1}{a}\\---------------\)
5. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{4}{5}}}\\= a^{ \frac{-1}{2} - \frac{4}{5} }= a^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ a^{13} }}\\=\frac{1}{|a|.\sqrt[10]{ a^{3} }}=\frac{1}{|a|.\sqrt[10]{ a^{3} }} \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{4}{5}}}\\= y^{ \frac{2}{3} - \frac{4}{5} }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
7. \(\dfrac{x^{1}}{x^{\frac{-5}{4}}}\\= x^{ 1 - (\frac{-5}{4}) }= x^{\frac{9}{4}}\\=\sqrt[4]{ x^{9} }=|x^{2}|.\sqrt[4]{ x }\\---------------\)
8. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{2}{5} - (\frac{-5}{2}) }= q^{\frac{29}{10}}\\=\sqrt[10]{ q^{29} }=|q^{2}|.\sqrt[10]{ q^{9} }\\---------------\)
9. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{3}{2}}}\\= y^{ \frac{-3}{4} - \frac{3}{2} }= y^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ y^{9} }}\\=\frac{1}{|y^{2}|.\sqrt[4]{ y }}=\frac{1}{|y^{2}|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{3}|}\\---------------\)
10. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{4}{5}}}\\= q^{ \frac{5}{2} - \frac{4}{5} }= q^{\frac{17}{10}}\\=\sqrt[10]{ q^{17} }=|q|.\sqrt[10]{ q^{7} }\\---------------\)
11. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{5}{3} - (\frac{-2}{3}) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
12. \(\dfrac{x^{\frac{3}{5}}}{x^{-1}}\\= x^{ \frac{3}{5} - (-1) }= x^{\frac{8}{5}}\\=\sqrt[5]{ x^{8} }=x.\sqrt[5]{ x^{3} }\\---------------\)