Macht van een macht

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{3}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{3}{2} . (\frac{-1}{2}) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
2. \(\left(a^{\frac{1}{2}}\right)^{-1}\\= a^{ \frac{1}{2} . (-1) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
3. \(\left(y^{1}\right)^{\frac{-5}{2}}\\= y^{ 1 . (\frac{-5}{2}) }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
4. \(\left(q^{\frac{-5}{3}}\right)^{1}\\= q^{ \frac{-5}{3} . 1 }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
5. \(\left(q^{\frac{-4}{3}}\right)^{\frac{-5}{4}}\\= q^{ \frac{-4}{3} . (\frac{-5}{4}) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
6. \(\left(y^{\frac{2}{5}}\right)^{\frac{-5}{2}}\\= y^{ \frac{2}{5} . (\frac{-5}{2}) }= y^{-1}\\=\frac{1}{y}\\---------------\)
7. \(\left(x^{-2}\right)^{\frac{2}{3}}\\= x^{ -2 . \frac{2}{3} }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
8. \(\left(x^{\frac{-1}{4}}\right)^{\frac{-1}{4}}\\= x^{ \frac{-1}{4} . (\frac{-1}{4}) }= x^{\frac{1}{16}}\\=\sqrt[16]{ x }\\---------------\)
9. \(\left(a^{1}\right)^{\frac{-4}{5}}\\= a^{ 1 . (\frac{-4}{5}) }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)
10. \(\left(y^{\frac{4}{3}}\right)^{2}\\= y^{ \frac{4}{3} . 2 }= y^{\frac{8}{3}}\\=\sqrt[3]{ y^{8} }=y^{2}.\sqrt[3]{ y^{2} }\\---------------\)
11. \(\left(x^{\frac{3}{4}}\right)^{\frac{3}{4}}\\= x^{ \frac{3}{4} . \frac{3}{4} }= x^{\frac{9}{16}}\\=\sqrt[16]{ x^{9} }\\---------------\)
12. \(\left(y^{\frac{5}{3}}\right)^{\frac{-2}{3}}\\= y^{ \frac{5}{3} . (\frac{-2}{3}) }= y^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ y^{10} }}\\=\frac{1}{y.\sqrt[9]{ y }}=\frac{1}{y.\sqrt[9]{ y }} \color{purple}{\frac{\sqrt[9]{ y^{8} }}{\sqrt[9]{ y^{8} }}} \\=\frac{\sqrt[9]{ y^{8} }}{y^{2}}\\---------------\)