Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{-5}{3} - (\frac{-3}{2}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
2. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{1}{3} - (\frac{-4}{5}) }= y^{\frac{17}{15}}\\=\sqrt[15]{ y^{17} }=y.\sqrt[15]{ y^{2} }\\---------------\)
3. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{-3}{2} - (\frac{-3}{2}) }= x^{0}\\=1\\---------------\)
4. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{5}{6}}}\\= y^{ \frac{1}{2} - \frac{5}{6} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
5. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{1}{4}}}\\= q^{ \frac{1}{3} - \frac{1}{4} }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)
6. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{3}{2}}}\\= q^{ \frac{-1}{2} - \frac{3}{2} }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
7. \(\dfrac{x^{1}}{x^{\frac{4}{5}}}\\= x^{ 1 - \frac{4}{5} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
8. \(\dfrac{y^{\frac{3}{4}}}{y^{-1}}\\= y^{ \frac{3}{4} - (-1) }= y^{\frac{7}{4}}\\=\sqrt[4]{ y^{7} }=|y|.\sqrt[4]{ y^{3} }\\---------------\)
9. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-5}{4} - \frac{1}{2} }= a^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[4]{ a^{3} }}=\frac{1}{|a|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{2}|}\\---------------\)
10. \(\dfrac{a^{1}}{a^{\frac{-5}{4}}}\\= a^{ 1 - (\frac{-5}{4}) }= a^{\frac{9}{4}}\\=\sqrt[4]{ a^{9} }=|a^{2}|.\sqrt[4]{ a }\\---------------\)
11. \(\dfrac{x^{-1}}{x^{\frac{-2}{3}}}\\= x^{ -1 - (\frac{-2}{3}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
12. \(\dfrac{x^{\frac{-4}{3}}}{x^{1}}\\= x^{ \frac{-4}{3} - 1 }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)