(21x^-2)^0
When any non-zero number is raised to the power of zero, the result is always 1. Therefore, (21x^-2)^0 = 1.
3x^2 times (1/7)x^-2
To multiply two terms with the same base (in this case, x), you add their exponents.
So, 3x^2 multiplied by (1/7)x^-2 would be equal to 3/7x^(2 + (-2)).
The exponent of x becomes 2 + (-2) = 0, resulting in:
3/7x^0
Any non-zero number raised to the power of zero is always 1.
Thus, the final simplified expression is 3/7.