Werk uit m.b.v. de rekenregels
- \(y^{1}.y^{\frac{-1}{2}}\)
- \(q^{1}.q^{\frac{4}{3}}\)
- \(a^{-2}.a^{\frac{5}{3}}\)
- \(x^{\frac{2}{3}}.x^{\frac{-1}{3}}\)
- \(a^{\frac{1}{3}}.a^{\frac{-3}{4}}\)
- \(a^{\frac{1}{2}}.a^{\frac{-3}{2}}\)
- \(x^{\frac{-3}{5}}.x^{\frac{3}{5}}\)
- \(a^{\frac{2}{3}}.a^{\frac{-1}{2}}\)
- \(a^{-2}.a^{\frac{-5}{3}}\)
- \(y^{\frac{1}{2}}.y^{\frac{1}{3}}\)
- \(q^{\frac{1}{2}}.q^{\frac{1}{6}}\)
- \(y^{\frac{1}{5}}.y^{\frac{-1}{2}}\)
Werk uit m.b.v. de rekenregels
Verbetersleutel
- \(y^{1}.y^{\frac{-1}{2}}\\= y^{ 1 + (\frac{-1}{2}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
- \(q^{1}.q^{\frac{4}{3}}\\= q^{ 1 + \frac{4}{3} }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
- \(a^{-2}.a^{\frac{5}{3}}\\= a^{ -2 + \frac{5}{3} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}.
\color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
- \(x^{\frac{2}{3}}.x^{\frac{-1}{3}}\\= x^{ \frac{2}{3} + (\frac{-1}{3}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
- \(a^{\frac{1}{3}}.a^{\frac{-3}{4}}\\= a^{ \frac{1}{3} + (\frac{-3}{4}) }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}.
\color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
- \(a^{\frac{1}{2}}.a^{\frac{-3}{2}}\\= a^{ \frac{1}{2} + (\frac{-3}{2}) }= a^{-1}\\=\frac{1}{a}\\---------------\)
- \(x^{\frac{-3}{5}}.x^{\frac{3}{5}}\\= x^{ \frac{-3}{5} + \frac{3}{5} }= x^{0}\\=1\\---------------\)
- \(a^{\frac{2}{3}}.a^{\frac{-1}{2}}\\= a^{ \frac{2}{3} + (\frac{-1}{2}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
- \(a^{-2}.a^{\frac{-5}{3}}\\= a^{ -2 + (\frac{-5}{3}) }= a^{\frac{-11}{3}}\\=\frac{1}{\sqrt[3]{ a^{11} }}\\=\frac{1}{a^{3}.\sqrt[3]{ a^{2} }}=\frac{1}{a^{3}.\sqrt[3]{ a^{2} }}
\color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{4}}\\---------------\)
- \(y^{\frac{1}{2}}.y^{\frac{1}{3}}\\= y^{ \frac{1}{2} + \frac{1}{3} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
- \(q^{\frac{1}{2}}.q^{\frac{1}{6}}\\= q^{ \frac{1}{2} + \frac{1}{6} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
- \(y^{\frac{1}{5}}.y^{\frac{-1}{2}}\\= y^{ \frac{1}{5} + (\frac{-1}{2}) }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}.
\color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)