D is correct.
In A, 3x^0 = 3*1 = 3, while (3x)^0 = 1
(assuming x is not zero)
Which of the following statements most accurately describes the difference between 3x^0 and (3x)^0, if a difference exists?
A. There is no mathematical difference between 3x^0 and (3x)^0. The two are equivalent expressions.
B. In the expression 3x^0, the exponent 0 is applied only to the variable x, while in (3x)^0, the exponent 0 is applied only to the coefficient 3.
C. In the expression (3x)^0, the exponent is applied only to the variable x, while in 3x^0, the exponent 0 is applied to both the variable x and the coefficient 3.
D. In the expression 3x^0, the exponent 0 is applied only to the variable x, while in (3x)^0, the exponent 0 is applied to both the variable x and the coefficient 3.
I know the answer is not C, but I think the answer is either A or D. Can someone please check?
Please help me by checking. Any help will be greatly appreciated! :)
P.S. Please reply as soon as possible! Thank you, and there may be a few more.
In A, 3x^0 = 3*1 = 3, while (3x)^0 = 1
(assuming x is not zero)
In this case, the exponent 0 is applied to the expressions 3x^0 and (3x)^0. Any nonzero number raised to the power of zero is equal to 1. So we need to determine if any part of the expression has a nonzero number.
Let's analyze each of the given options:
A. There is no mathematical difference between 3x^0 and (3x)^0. The two are equivalent expressions.
B. In the expression 3x^0, the exponent 0 is applied only to the variable x, while in (3x)^0, the exponent 0 is applied only to the coefficient 3.
C. In the expression (3x)^0, the exponent is applied only to the variable x, while in 3x^0, the exponent 0 is applied to both the variable x and the coefficient 3.
D. In the expression 3x^0, the exponent 0 is applied only to the variable x, while in (3x)^0, the exponent 0 is applied to both the variable x and the coefficient 3.
Based on the properties of exponents, option A is correct. In both 3x^0 and (3x)^0, the exponent 0 is applied only to the variable x. The coefficient 3 is not affected by the exponent in either expression.
Therefore, the most accurate statement is A: There is no mathematical difference between 3x^0 and (3x)^0. The two are equivalent expressions.
I hope this clarifies your doubt!