Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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