How do you simplify #3^(1/4) * 4^(1/4)#?

Answer 1

Julia Adams

The answer is #root(4)12#.

Because of the commutative and associative properties of multiplication, you can rewrite #a^(x)*b^(x)# as #(ab)^x#

Therefore, #3^(1/4)*4^(1/4) = 12^(1/4)#.

We also know that #a^(1/x) = root(x)a#.

Thus, #12^(1/4) = root(4)12 = root(4)(2*2*3)#.

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Answer 2

Julia Adams

To simplify 3^(1/4) * 4^(1/4), you can rewrite 4 as 2^2. Then, using the property of exponents, you can simplify the expression as (3 * 2^2)^(1/4). This further simplifies to (12)^(1/4). Finally, applying the exponent rule for radicals, the simplified expression is the fourth root of 12.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.