Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{3}{4}}}\\= x^{ \frac{5}{2} - \frac{3}{4} }= x^{\frac{7}{4}}\\=\sqrt[4]{ x^{7} }=|x|.\sqrt[4]{ x^{3} }\\---------------\)
2. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{1}{4} - (\frac{-5}{6}) }= a^{\frac{13}{12}}\\=\sqrt[12]{ a^{13} }=|a|.\sqrt[12]{ a }\\---------------\)
3. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-4}{3} - \frac{5}{4} }= y^{\frac{-31}{12}}\\=\frac{1}{\sqrt[12]{ y^{31} }}\\=\frac{1}{|y^{2}|.\sqrt[12]{ y^{7} }}=\frac{1}{|y^{2}|.\sqrt[12]{ y^{7} }} \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y^{3}|}\\---------------\)
4. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-1}{2} - \frac{1}{2} }= q^{-1}\\=\frac{1}{q}\\---------------\)
5. \(\dfrac{x^{1}}{x^{\frac{1}{4}}}\\= x^{ 1 - \frac{1}{4} }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
6. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-1}{3} - \frac{5}{4} }= x^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ x^{19} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{7} }}=\frac{1}{|x|.\sqrt[12]{ x^{7} }} \color{purple}{\frac{\sqrt[12]{ x^{5} }}{\sqrt[12]{ x^{5} }}} \\=\frac{\sqrt[12]{ x^{5} }}{|x^{2}|}\\---------------\)
7. \(\dfrac{a^{-1}}{a^{\frac{-2}{3}}}\\= a^{ -1 - (\frac{-2}{3}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
8. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{5}{3}}}\\= q^{ \frac{1}{3} - \frac{5}{3} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
9. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{1}{4}}}\\= y^{ \frac{1}{2} - \frac{1}{4} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
10. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{4}{3} - (\frac{-4}{3}) }= a^{\frac{8}{3}}\\=\sqrt[3]{ a^{8} }=a^{2}.\sqrt[3]{ a^{2} }\\---------------\)
11. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-5}{4} - (\frac{-1}{2}) }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
12. \(\dfrac{y^{\frac{-1}{5}}}{y^{-1}}\\= y^{ \frac{-1}{5} - (-1) }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)