How do you simplify $3^{\frac{1}{4}} \cdot 4^{\frac{1}{4}}$ $3^(1/4) * 4^(1/4)$ ?

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Answer 1 · 2015-05-17T08:51:45

The answer is $\sqrt[4]{12}$ $root(4)12$ .

Because of the commutative and associative properties of multiplication, you can rewrite $a^{x} \cdot b^{x}$ $a^(x)*b^(x)$ as ${(a b)}^{x}$ $(ab)^x$

Therefore, $3^{\frac{1}{4}} \cdot 4^{\frac{1}{4}} = 12^{\frac{1}{4}}$ $3^(1/4)*4^(1/4) = 12^(1/4)$ .

We also know that $a^{\frac{1}{x}} = \sqrt[x]{a}$ $a^(1/x) = root(x)a$ .

Thus, $12^{\frac{1}{4}} = \sqrt[4]{12} = \sqrt[4]{2 \cdot 2 \cdot 3}$ $12^(1/4) = root(4)12 = root(4)(2*2*3)$ .

How do you simplify 314⋅4143^(1/4) * 4^(1/4)?