To simplify \( (21x^{-2})^0 \), we need to recognize that any non-zero number raised to the power of 0 is equal to 1. Therefore:
\[ (21x^{-2})^0 = 1 \]
Now, let's evaluate the options given:
A. \( 3x^2 \cdot \frac{1}{7} x^{-2} \)
- This expression simplifies but does not equal 1.
B. \( \frac{7x^2}{7x^2} \)
- This expression simplifies to 1 (as long as \( x \neq 0 \)).
C. \( (21x^{12} y)^1 \)
- This is equal to \( 21x^{12} y \), which is not equal to 1.
D. \( 0x^2 \cdot 21x^4 \)
- This equals 0, which is not equal to 1.
Among these options, the only expression that is equivalent to \( (21x^{-2})^0 = 1 \) is:
B. \( \frac{7x^2}{7x^2} \).
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