Werk uit m.b.v. de rekenregels
- \(y^{\frac{-3}{5}}.y^{\frac{-4}{3}}\)
- \(a^{\frac{4}{3}}.a^{\frac{4}{3}}\)
- \(x^{\frac{-2}{3}}.x^{\frac{5}{6}}\)
- \(y^{\frac{1}{6}}.y^{\frac{1}{5}}\)
- \(y^{\frac{-1}{2}}.y^{1}\)
- \(q^{\frac{-3}{5}}.q^{\frac{-3}{4}}\)
- \(x^{\frac{1}{2}}.x^{\frac{5}{2}}\)
- \(y^{\frac{1}{3}}.y^{\frac{2}{3}}\)
- \(y^{\frac{2}{3}}.y^{\frac{1}{5}}\)
- \(a^{\frac{4}{3}}.a^{1}\)
- \(y^{\frac{-1}{5}}.y^{\frac{3}{4}}\)
- \(x^{1}.x^{\frac{5}{4}}\)
Werk uit m.b.v. de rekenregels
Verbetersleutel
- \(y^{\frac{-3}{5}}.y^{\frac{-4}{3}}\\= y^{ \frac{-3}{5} + (\frac{-4}{3}) }= y^{\frac{-29}{15}}\\=\frac{1}{\sqrt[15]{ y^{29} }}\\=\frac{1}{y.\sqrt[15]{ y^{14} }}=\frac{1}{y.\sqrt[15]{ y^{14} }}
\color{purple}{\frac{\sqrt[15]{ y }}{\sqrt[15]{ y }}} \\=\frac{\sqrt[15]{ y }}{y^{2}}\\---------------\)
- \(a^{\frac{4}{3}}.a^{\frac{4}{3}}\\= a^{ \frac{4}{3} + \frac{4}{3} }= a^{\frac{8}{3}}\\=\sqrt[3]{ a^{8} }=a^{2}.\sqrt[3]{ a^{2} }\\---------------\)
- \(x^{\frac{-2}{3}}.x^{\frac{5}{6}}\\= x^{ \frac{-2}{3} + \frac{5}{6} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
- \(y^{\frac{1}{6}}.y^{\frac{1}{5}}\\= y^{ \frac{1}{6} + \frac{1}{5} }= y^{\frac{11}{30}}\\=\sqrt[30]{ y^{11} }\\---------------\)
- \(y^{\frac{-1}{2}}.y^{1}\\= y^{ \frac{-1}{2} + 1 }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
- \(q^{\frac{-3}{5}}.q^{\frac{-3}{4}}\\= q^{ \frac{-3}{5} + (\frac{-3}{4}) }= q^{\frac{-27}{20}}\\=\frac{1}{\sqrt[20]{ q^{27} }}\\=\frac{1}{|q|.\sqrt[20]{ q^{7} }}=\frac{1}{|q|.\sqrt[20]{ q^{7} }}
\color{purple}{\frac{\sqrt[20]{ q^{13} }}{\sqrt[20]{ q^{13} }}} \\=\frac{\sqrt[20]{ q^{13} }}{|q^{2}|}\\---------------\)
- \(x^{\frac{1}{2}}.x^{\frac{5}{2}}\\= x^{ \frac{1}{2} + \frac{5}{2} }= x^{3}\\\\---------------\)
- \(y^{\frac{1}{3}}.y^{\frac{2}{3}}\\= y^{ \frac{1}{3} + \frac{2}{3} }= y^{1}\\\\---------------\)
- \(y^{\frac{2}{3}}.y^{\frac{1}{5}}\\= y^{ \frac{2}{3} + \frac{1}{5} }= y^{\frac{13}{15}}\\=\sqrt[15]{ y^{13} }\\---------------\)
- \(a^{\frac{4}{3}}.a^{1}\\= a^{ \frac{4}{3} + 1 }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
- \(y^{\frac{-1}{5}}.y^{\frac{3}{4}}\\= y^{ \frac{-1}{5} + \frac{3}{4} }= y^{\frac{11}{20}}\\=\sqrt[20]{ y^{11} }\\---------------\)
- \(x^{1}.x^{\frac{5}{4}}\\= x^{ 1 + \frac{5}{4} }= x^{\frac{9}{4}}\\=\sqrt[4]{ x^{9} }=|x^{2}|.\sqrt[4]{ x }\\---------------\)