Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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