Algebra Question Please Help!

Question

Simplify: (⁴√3 ³√3)

(A) (3 ⁴√3)

(B) 4√27

(C) 3√3

(D) 7√27

(E) none of these

The answer I got is (E) none of these. But, I still got it wrong. Can someone please explain to me what was done wrong?

Answer 1

Answer 2

You are correct.

We can simplify this problem by using fractional exponents and then using the properties of exponents to combine.

⁴√3 = 3^1/4

³√3 = 3^1/3

So ⁴√3³√3 = 3^1/4•3^1/3

One of the properties of exponents is that when the bases are the same, we add the exponents so:

3^1/4•3^1/3 = 3^{1/4 + 1/3} = 3^{3/12 + 4/12} = 3^7/12 = ¹²√3⁷ ≈ 1.898

The answers listed have the following decimal approximations:

(A) 3• ⁴√3 ≈ 3.948

(B) 4√27 ≈ 20.785 (even if we consider this as ⁴√27, it still equates to 2.28)

(C) 3√3 ≈ 5.196 (even if we consider this as ³√3, it still equates to 1.44)

(D) 7√27 ≈ 36.373 (even if we consider this as ⁷√27, it still equates to 1.601)

So I see none of the answers that could possibly be right