Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{1}{4}}}\\= y^{ \frac{-3}{4} - \frac{1}{4} }= y^{-1}\\=\frac{1}{y}\\---------------\)
2. \(\dfrac{a^{1}}{a^{\frac{3}{4}}}\\= a^{ 1 - \frac{3}{4} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
3. \(\dfrac{x^{-2}}{x^{\frac{-1}{4}}}\\= x^{ -2 - (\frac{-1}{4}) }= x^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[4]{ x^{3} }}=\frac{1}{|x|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{-5}{4} - (\frac{-1}{4}) }= y^{-1}\\=\frac{1}{y}\\---------------\)
5. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{5}{6} - (\frac{-1}{3}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
6. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{-1}{6} - (\frac{-1}{4}) }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)
7. \(\dfrac{x^{\frac{2}{5}}}{x^{1}}\\= x^{ \frac{2}{5} - 1 }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)
8. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{3}{4}}}\\= x^{ \frac{5}{2} - \frac{3}{4} }= x^{\frac{7}{4}}\\=\sqrt[4]{ x^{7} }=|x|.\sqrt[4]{ x^{3} }\\---------------\)
9. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-4}{5} - (\frac{-2}{3}) }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
10. \(\dfrac{a^{\frac{4}{3}}}{a^{1}}\\= a^{ \frac{4}{3} - 1 }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{3}{4}}}\\= a^{ \frac{1}{2} - \frac{3}{4} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
12. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-5}{6} - (\frac{-3}{5}) }= x^{\frac{-7}{30}}\\=\frac{1}{\sqrt[30]{ x^{7} }}=\frac{1}{\sqrt[30]{ x^{7} }}. \color{purple}{\frac{\sqrt[30]{ x^{23} }}{\sqrt[30]{ x^{23} }}} \\=\frac{\sqrt[30]{ x^{23} }}{|x|}\\---------------\)