Question

Proszę o obliczenie tych 4 przykładów krok po kroku.

Daje naj liczę na pomoc

Answer 1

[tex]3^{\frac{3}{2}}:\sqrt3=3^{\frac{3}{2}}:3^{\frac{1}{2}}=3^{\frac{3}{2}-\frac{1}{2}}=3^{\frac{2}{2}}=3^1=3\\\\\\\left(25\sqrt5\right):5^{\frac{3}{2}}=\left(5^2*5^{\frac{1}{2}\right):5^{\frac{3}{2}}=5^{2+\frac{1}{2}}:5^{\frac{3}{2}}=5^{2\frac{1}{2}}:5^{1\frac{1}{2}}=5^{2\frac{1}{2}-1\frac{1}{2}}=5^1=5\\\\\\15^{0,5}*0,36^{0,25}=15^{0,5}*\left((0,6)^2\right)^{0,25}=15^{0,5}*(0,6)^{2*0,25}=15^{0,5}*(0,6)^{0,5}=\\=(15*0,6)^{0,5}=9^{0,5}=9^{\frac{1}{2}}=\sqrt9=3[/tex]

[tex]20^\frac{1}{3}*2,5^{-\frac{1}{3}}=20^\frac{1}{3}*\left(2\frac{1}{2}\right)^{-\frac{1}{3}}=20^\frac{1}{3}*\left(\frac{5}{2}\right)^{-\frac{1}{3}}=20^\frac{1}{3}*\left(\frac{2}{5}\right)^{\frac{1}{3}}=\left(20*\frac{2}{5}\right)^{\frac{1}{3}}=\\=\left(4*\frac{2}{1}\right)^{\frac{1}{3}}=8^{\frac{1}{3}}=\sqrt[3]8=2[/tex]