Determine whether each of the following expressions is equivalent to x 8/3.
Answer Choices:
1. ( ( ∛x)^4)^2
2. ∛x 4 ⋅ ∛x4
3.(∛x)^0/(∛x^2)^-4
4. 8^√ x^3
To determine if each of the expressions is equivalent to x 8/3, we can simplify each expression and see if it simplifies to x 8/3.
1. ( ( ∛x)^4)^2 = (∛x)^8 = x 8/3. This expression is equivalent to x 8/3.
2. ∛x 4 ⋅ ∛x4 = ∛x^(4+4) = ∛x^8 = x 8/3. This expression is also equivalent to x 8/3.
3. (∛x)^0/(∛x^2)^-4 = 1/((∛x^2)^4) = 1/(x^(2/3 * 4)) = 1/x^(8/3) ≠ x 8/3. This expression is not equivalent to x 8/3.
4. 8^√ x^3 = (2^3)^√x^3 = 2^6√x^3 = 2^(6/2) x^3/2 = x^3/2 x^3/2 = x^6/4. This expression is not equivalent to x 8/3.
Only the first two expressions are equivalent to x 8/3.