Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{1}{4} - (\frac{-3}{5}) }= a^{\frac{17}{20}}\\=\sqrt[20]{ a^{17} }\\---------------\)
2. \(\dfrac{y^{-1}}{y^{\frac{-4}{3}}}\\= y^{ -1 - (\frac{-4}{3}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
3. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{5} - \frac{1}{2} }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
4. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-1}{2} - (\frac{-3}{5}) }= x^{\frac{1}{10}}\\=\sqrt[10]{ x }\\---------------\)
5. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{-1}{2} - (\frac{-1}{4}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
6. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{3}{2} - (\frac{-2}{3}) }= x^{\frac{13}{6}}\\=\sqrt[6]{ x^{13} }=|x^{2}|.\sqrt[6]{ x }\\---------------\)
7. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{2}{3}}}\\= a^{ \frac{1}{2} - \frac{2}{3} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
8. \(\dfrac{y^{\frac{5}{6}}}{y^{-2}}\\= y^{ \frac{5}{6} - (-2) }= y^{\frac{17}{6}}\\=\sqrt[6]{ y^{17} }=|y^{2}|.\sqrt[6]{ y^{5} }\\---------------\)
9. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{1}{4} - (\frac{-1}{6}) }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
10. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{4}{5}}}\\= q^{ \frac{-2}{3} - \frac{4}{5} }= q^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ q^{22} }}\\=\frac{1}{q.\sqrt[15]{ q^{7} }}=\frac{1}{q.\sqrt[15]{ q^{7} }} \color{purple}{\frac{\sqrt[15]{ q^{8} }}{\sqrt[15]{ q^{8} }}} \\=\frac{\sqrt[15]{ q^{8} }}{q^{2}}\\---------------\)
11. \(\dfrac{a^{1}}{a^{\frac{5}{4}}}\\= a^{ 1 - \frac{5}{4} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
12. \(\dfrac{a^{-1}}{a^{\frac{5}{4}}}\\= a^{ -1 - \frac{5}{4} }= a^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ a^{9} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a }}=\frac{1}{|a^{2}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{3}|}\\---------------\)