Answer: To determine which expression is equivalent to 3√/8x²y³ z^4, we need to simplify the given expression and compare it with the options.
First, we can simplify the cube root:
3√/8x²y³ z^4 = (3/8)x^(2/3)y^(1/3)z^(4/3)
Now, we can compare this expression with the options:
A. 2x^(3/2)YZ^(3/4) is not equivalent to the simplified expression because the exponent of x is different (3/2 vs 2/3)
B. 2x^(2/3)YZ^(3/4) is equivalent to the simplified expression. The exponents of x, y and z are the same and the coefficient is also the same
C. 2z/x is not equivalent to the simplified expression because it has different variables and exponents
D. 2x/z is not equivalent to the simplified expression because it has different variables and exponents
Therefore, the expression that is equivalent to 3√/8x²y³ z^4 is B. 2x^(2/3)YZ^(3/4)
Explanation: