Question

Which statement is true?

A. In the expression 8x18x is the radicand.
B. In the expression (-16)x, 4 is the index.
C. The expression 1024√ represents the mth root of the nth power of 1024.
D. 50⁻⁵ = -503
E. ſ(x) = xy?

Answer 1

All statements provided are false; the expressions either misrepresent or do not provide enough information to identify true mathematical terms such as the radicand, index, or roots. option C is the correct answer.

Step-by-step explanation:

The question is asking to identify which statement is true regarding powers and roots in mathematical expressions. Let's evaluate each statement:

1. A: In the expression 8x18, 'x' is actually the variable and '8' would be the coefficient if this was an algebraic expression. However, as presented, this expression is incomplete and does not contain a radicand or specify a radical, making this statement false.
2. B: In the expression (-16)x, we would need to see an expression like root(4, -16) to identify 4 as the index of a radical. The given expression does not present 4 as the index, rendering this statement false.
3. C: The expression 1024√ is also incomplete and does not provide enough information to infer a true mth root of the nth power. There are no exponents or indexes provided, so we cannot affirm this statement as true.
4. D: For the expression 50−5, this is an example of an "inversion," where the negative exponent means to take the reciprocal. So, 50−5 = 1/505 and not -503. Thus, this statement is false.
5. E: The expression √(x) = xy? is not meaningful without further context or clarification on what the symbols represent. Typically, √ symbol denotes a square root, and this expression would not be a standard way to represent a square root or any other root operation. This statement is therefore false.

Since all statements presented are false, there is no true statement among the options given.