The expression \((21x^{-2})^0\) is equal to 1, because any non-zero value raised to the power of 0 is equal to 1.
Now, let's evaluate the options:
A. \((21x^{12}y)^0 = 1\) (non-zero value raised to 0) B. \(\frac{7x^2}{7x^2} = 1\) (as long as \(x \neq 0\)) C. \(3x^2 \cdot \frac{1}{7} \cdot x^{-2} = \frac{3}{7}\) (not equal to 1) D. \(0x^2 \cdot 21x^4 = 0\) (because anything multiplied by 0 is 0)
The expressions that are equivalent to \((21x^{-2})^0 = 1\) are:
- A: \((21x^{12}y)^0\)
- B: \(\frac{7x^2}{7x^2}\)
So the correct options that are equivalent to \((21x^{-2})^0\) are A and B.