Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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