Question

Simplify the following equations

Answer 1

Step-by-step explanation:

Given the expressions

1)

$\sqrt[5]{16} * \sqrt[5]{2} \\= 16^{1/5} * 2^{1/5}\\= 2^{4(1/5)} * 2^{1/5}\\= 2^{4/5} * 2^{1/5}\\= 2^{4/5+1/5}\\= 2 ^{5/5}\\= 2^1\\= 2$

2)

$\frac{\sqrt[4]{243}}{\sqrt[4]{3}} \\= \frac{243^{1/4}}{3^{1/4}}\\= \frac{3^{5/4}}{3^{1/4}}\\=3^{5/4-1/4}\\= 3^{4/4}\\= 3$

3)

$(3+\sqrt{2} )(4+\sqrt{7} )\\= 3(4) + 3\sqrt{7} + 4\sqrt{2} + \sqrt{14} \\= 12 + 3\sqrt{7} + 4\sqrt{2} + \sqrt{14}$