Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{-1}}{x^{\frac{-3}{2}}}\\= x^{ -1 - (\frac{-3}{2}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
2. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{1}{6}}}\\= y^{ \frac{2}{3} - \frac{1}{6} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
3. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{3}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
4. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{1}{2} - (\frac{-4}{5}) }= q^{\frac{13}{10}}\\=\sqrt[10]{ q^{13} }=|q|.\sqrt[10]{ q^{3} }\\---------------\)
5. \(\dfrac{y^{1}}{y^{\frac{3}{4}}}\\= y^{ 1 - \frac{3}{4} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
6. \(\dfrac{q^{\frac{3}{2}}}{q^{-1}}\\= q^{ \frac{3}{2} - (-1) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
7. \(\dfrac{a^{-1}}{a^{-1}}\\= a^{ -1 - (-1) }= a^{0}\\=1\\---------------\)
8. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{5}{2}}}\\= x^{ \frac{5}{3} - \frac{5}{2} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
9. \(\dfrac{x^{\frac{1}{2}}}{x^{-1}}\\= x^{ \frac{1}{2} - (-1) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
10. \(\dfrac{q^{-1}}{q^{\frac{-4}{5}}}\\= q^{ -1 - (\frac{-4}{5}) }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
11. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{5}{2}}}\\= a^{ \frac{-4}{3} - \frac{5}{2} }= a^{\frac{-23}{6}}\\=\frac{1}{\sqrt[6]{ a^{23} }}\\=\frac{1}{|a^{3}|.\sqrt[6]{ a^{5} }}=\frac{1}{|a^{3}|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{4}|}\\---------------\)
12. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{4}{3} - \frac{1}{3} }= y^{1}\\\\---------------\)