Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{-5}{3} - (\frac{-5}{3}) }= x^{0}\\=1\\---------------\)
2. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{-2}{5} - (\frac{-3}{4}) }= q^{\frac{7}{20}}\\=\sqrt[20]{ q^{7} }\\---------------\)
3. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{3}{4} - (\frac{-5}{2}) }= y^{\frac{13}{4}}\\=\sqrt[4]{ y^{13} }=|y^{3}|.\sqrt[4]{ y }\\---------------\)
4. \(\dfrac{x^{\frac{-1}{4}}}{x^{-1}}\\= x^{ \frac{-1}{4} - (-1) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
5. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{3}{2}}}\\= x^{ \frac{-4}{3} - \frac{3}{2} }= x^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ x^{17} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x^{5} }}=\frac{1}{|x^{2}|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{3}|}\\---------------\)
6. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{5}{3}}}\\= y^{ \frac{-3}{4} - \frac{5}{3} }= y^{\frac{-29}{12}}\\=\frac{1}{\sqrt[12]{ y^{29} }}\\=\frac{1}{|y^{2}|.\sqrt[12]{ y^{5} }}=\frac{1}{|y^{2}|.\sqrt[12]{ y^{5} }} \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y^{3}|}\\---------------\)
7. \(\dfrac{q^{1}}{q^{\frac{1}{2}}}\\= q^{ 1 - \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
8. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{5}{2} - (\frac{-4}{3}) }= x^{\frac{23}{6}}\\=\sqrt[6]{ x^{23} }=|x^{3}|.\sqrt[6]{ x^{5} }\\---------------\)
9. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{1}{5}}}\\= x^{ \frac{-3}{5} - \frac{1}{5} }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)
10. \(\dfrac{x^{1}}{x^{\frac{5}{4}}}\\= x^{ 1 - \frac{5}{4} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
11. \(\dfrac{q^{\frac{-5}{6}}}{q^{-1}}\\= q^{ \frac{-5}{6} - (-1) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
12. \(\dfrac{y^{1}}{y^{\frac{-2}{3}}}\\= y^{ 1 - (\frac{-2}{3}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)