fully simplify (z^-2/cdotz^8)^2

Answer 1

To simplify the expression, we can start by simplifying the inside of the parentheses.

(z^-2/cdotz^8)^2 = [(1/z^2) * (1/z^8)]^2

Next, we can simplify the expression in the square brackets by combining the fractions:

[(1/z^2) * (1/z^8)]^2 = (1/z^10)^2

To raise a fraction to the power of 2, we square both the numerator and denominator:

(1/z^10)^2 = (1^2)/(z^10)^2 = 1/(z^20)

Therefore, the fully simplified expression is 1/(z^20).

Answer 2

wrong

Answer 3

Apologies for the mistake in the previous response. Let's simplify the expression correctly.

To simplify (z^-2 ⋅ z^8)^2, we can use the property (a ⋅ b)^n = a^n ⋅ b^n.

First, simplify the expression inside the parentheses:
z^-2 ⋅ z^8 = z^(-2 + 8) = z^6

Now, raise z^6 to the power of 2:
(z^6)^2 = z^(6 ⋅ 2) = z^12

Therefore, the fully simplified expression is z^12.