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

Question

?(1 point)
Responses

(21x^12y)^1
open paren 21 x to the 12th power y close paren to the 1th power

0x2^⋅21x^4
0 times x squared times 21 x to the 4th power

3x^2⋅(1/7)x^−2
3 times x squared times 1 seventh x to the negative 2 power

7x^2/7x^2

Answer 1

To evaluate the expression \((21x^{-2})^0\), we can apply the zero exponent rule, which states that any non-zero number raised to the power of zero is equal to 1.

Therefore, \((21x^{-2})^0 = 1\).

Now let's analyze the given responses:

1. \((21 x^{12} y)^1\) - This is equal to \(21 x^{12} y\) (not equivalent to 1).

2. \(0 \times x^2 \times 21 x^{4}\) - This equals 0 (not equivalent to 1).

3. \(3x^{2} \times \left(\frac{1}{7}\right)x^{-2}\) - This simplifies to \(3x^{2} \times \frac{1}{7} \times \frac{1}{x^{2}} = \frac{3}{7}\) (not equivalent to 1).

4. \(\frac{7x^{2}}{7x^{2}}\) - This simplifies to \(1\).

Thus, the expression that is equivalent to \((21x^{-2})^0\) is:

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