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

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