Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{3}{2}}}\\= y^{ \frac{3}{4} - \frac{3}{2} }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
2. \(\dfrac{x^{\frac{5}{3}}}{x^{1}}\\= x^{ \frac{5}{3} - 1 }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
3. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{-1}{3} - (\frac{-4}{5}) }= x^{\frac{7}{15}}\\=\sqrt[15]{ x^{7} }\\---------------\)
4. \(\dfrac{x^{\frac{-1}{5}}}{x^{-1}}\\= x^{ \frac{-1}{5} - (-1) }= x^{\frac{4}{5}}\\=\sqrt[5]{ x^{4} }\\---------------\)
5. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-1}{6} - \frac{2}{3} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
6. \(\dfrac{y^{\frac{1}{4}}}{y^{-1}}\\= y^{ \frac{1}{4} - (-1) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
7. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{6} - (\frac{-1}{2}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
8. \(\dfrac{x^{1}}{x^{\frac{-4}{3}}}\\= x^{ 1 - (\frac{-4}{3}) }= x^{\frac{7}{3}}\\=\sqrt[3]{ x^{7} }=x^{2}.\sqrt[3]{ x }\\---------------\)
9. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{3}{5} - (\frac{-3}{5}) }= a^{\frac{6}{5}}\\=\sqrt[5]{ a^{6} }=a.\sqrt[5]{ a }\\---------------\)
10. \(\dfrac{q^{\frac{-5}{4}}}{q^{-2}}\\= q^{ \frac{-5}{4} - (-2) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
11. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{1}{2}}}\\= y^{ \frac{1}{4} - \frac{1}{2} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
12. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{3}{5} - (\frac{-5}{4}) }= q^{\frac{37}{20}}\\=\sqrt[20]{ q^{37} }=|q|.\sqrt[20]{ q^{17} }\\---------------\)