Question

10в степени1/4 * 40 в степени 1/4 * 5 в степени 1/2=?

Answer 1

$10^{frac{1}{4}}*40^{frac{1}{4}}*5^{frac{1}{2}}=(10*40)^{frac{1}{4}}*5^{frac{1}{2}}=400^{frac{1}{4}}*5^{frac{1}{2}}=(20^2)^{frac{1}{4}}*5^{frac{1}{2}}=20^{2*frac{1}{4}}*5^{frac{1}{2}}=20^{frac{1}{2}}*5^{frac{1}{2}}=(20*5)^{frac{1}{2}}=100^{frac{1}{2}}=sqrt{100}=10$

Answer 2

$10^{frac {1}{4}} cdot 40^{frac {1}{4}} cdot 5^{frac {1}{2}}=sqrt [4]{10} cdot sqrt [4]{40} cdot sqrt [2]{5}=sqrt [4]{10cdot 40}cdot sqrt [2] 5=sqrt [4]{400} cdot sqrt [2]5 = \ \ = sqrt [2] {sqrt [2]{400}}cdot sqrt [2]5 =sqrt {sqrt {400}}cdot sqrt 5 =sqrt {20} cdot sqrt {5}=sqrt {20cdot 5}=sqrt {100}=10$