Question

Which expression is equivalent to (21x^−2)^0


A. 3x^2 *(1/7) x^-2
B. 7x^2/7x^2
C. (21x^12 y)^1
D. 0x^2 * 21x^4

Answer 1

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. \( \frac{7x^2}{7x^2} \)**.