fully simplify (z^-2/cdotz^8)^2
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).
wrong
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.
To simplify the expression (z^-2 ⋅ z^8)^2, we can apply the properties of exponents. Let's break it down step-by-step:
Step 1: Simplify the exponent inside the parentheses.
z^-2 ⋅ z^8
= z^(8 - 2) (Applying the rule a^m ⋅ a^n = a^(m+n))
= z^6
Step 2: Square the simplified expression.
(z^6)^2
= z^(6 ⋅ 2) (Applying the rule (a^m)^n = a^(m⋅n))
= z^12
Therefore, the fully simplified form of (z^-2 ⋅ z^8)^2 is z^12.