Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{5}{4}}}\\= q^{ \frac{5}{4} - \frac{5}{4} }= q^{0}\\=1\\---------------\)
2. \(\dfrac{q^{-1}}{q^{-1}}\\= q^{ -1 - (-1) }= q^{0}\\=1\\---------------\)
3. \(\dfrac{y^{\frac{-3}{2}}}{y^{-1}}\\= y^{ \frac{-3}{2} - (-1) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
4. \(\dfrac{q^{1}}{q^{\frac{-1}{3}}}\\= q^{ 1 - (\frac{-1}{3}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
5. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{-2}{3} - (\frac{-3}{4}) }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)
6. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{5}{4}}}\\= x^{ \frac{3}{5} - \frac{5}{4} }= x^{\frac{-13}{20}}\\=\frac{1}{\sqrt[20]{ x^{13} }}=\frac{1}{\sqrt[20]{ x^{13} }}. \color{purple}{\frac{\sqrt[20]{ x^{7} }}{\sqrt[20]{ x^{7} }}} \\=\frac{\sqrt[20]{ x^{7} }}{|x|}\\---------------\)
7. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{-1}{2} - (\frac{-1}{6}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
8. \(\dfrac{x^{-1}}{x^{\frac{-1}{6}}}\\= x^{ -1 - (\frac{-1}{6}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
9. \(\dfrac{y^{1}}{y^{1}}\\= y^{ 1 - 1 }= y^{0}\\=1\\---------------\)
10. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{1}{5}}}\\= q^{ \frac{2}{3} - \frac{1}{5} }= q^{\frac{7}{15}}\\=\sqrt[15]{ q^{7} }\\---------------\)
11. \(\dfrac{a^{\frac{1}{3}}}{a^{-2}}\\= a^{ \frac{1}{3} - (-2) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
12. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{3}{5}}}\\= q^{ \frac{-5}{3} - \frac{3}{5} }= q^{\frac{-34}{15}}\\=\frac{1}{\sqrt[15]{ q^{34} }}\\=\frac{1}{q^{2}.\sqrt[15]{ q^{4} }}=\frac{1}{q^{2}.\sqrt[15]{ q^{4} }} \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q^{3}}\\---------------\)