Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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