Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{3}{4}}}\\= x^{ \frac{1}{2} - \frac{3}{4} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
2. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{4}{3} - (\frac{-1}{3}) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
3. \(\dfrac{y^{1}}{y^{\frac{-5}{2}}}\\= y^{ 1 - (\frac{-5}{2}) }= y^{\frac{7}{2}}\\= \sqrt{ y^{7} } =|y^{3}|. \sqrt{ y } \\---------------\)
4. \(\dfrac{x^{-1}}{x^{\frac{-5}{3}}}\\= x^{ -1 - (\frac{-5}{3}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
5. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{1}{2} - (\frac{-3}{2}) }= a^{2}\\\\---------------\)
6. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{5}{4}}}\\= a^{ \frac{-3}{4} - \frac{5}{4} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
7. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-5}{3} - \frac{5}{4} }= y^{\frac{-35}{12}}\\=\frac{1}{\sqrt[12]{ y^{35} }}\\=\frac{1}{|y^{2}|.\sqrt[12]{ y^{11} }}=\frac{1}{|y^{2}|.\sqrt[12]{ y^{11} }} \color{purple}{\frac{\sqrt[12]{ y }}{\sqrt[12]{ y }}} \\=\frac{\sqrt[12]{ y }}{|y^{3}|}\\---------------\)
8. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{-4}{3} - (\frac{-3}{5}) }= a^{\frac{-11}{15}}\\=\frac{1}{\sqrt[15]{ a^{11} }}=\frac{1}{\sqrt[15]{ a^{11} }}. \color{purple}{\frac{\sqrt[15]{ a^{4} }}{\sqrt[15]{ a^{4} }}} \\=\frac{\sqrt[15]{ a^{4} }}{a}\\---------------\)
9. \(\dfrac{y^{\frac{-4}{5}}}{y^{-2}}\\= y^{ \frac{-4}{5} - (-2) }= y^{\frac{6}{5}}\\=\sqrt[5]{ y^{6} }=y.\sqrt[5]{ y }\\---------------\)
10. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{2}) }= y^{0}\\=1\\---------------\)
11. \(\dfrac{q^{-2}}{q^{\frac{-4}{3}}}\\= q^{ -2 - (\frac{-4}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
12. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-4}{3} - \frac{2}{3} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)