To find the value of [tex]\( y \)[/tex] such that the point [tex]\((-1, y)\)[/tex] lies on the graph of the function [tex]\( y = 2^{2x} \)[/tex], we need to substitute [tex]\( x = -1 \)[/tex] into the equation and solve for [tex]\( y \)[/tex].
Given [tex]\( y = 2^{2x} \)[/tex]:
1. Substitute [tex]\( x = -1 \)[/tex] into the equation:
[tex]\[
y = 2^{2(-1)}
\][/tex]
2. Simplify the exponent:
[tex]\[
y = 2^{-2}
\][/tex]
3. Simplify the expression using the negative exponent rule [tex]\(\left(a^{-n} = \frac{1}{a^n}\right)\)[/tex]:
[tex]\[
2^{-2} = \frac{1}{2^2}
\][/tex]
4. Calculate the exponent in the denominator:
[tex]\[
\frac{1}{2^2} = \frac{1}{4}
\][/tex]
Therefore, the value of [tex]\( y \)[/tex] is:
\[
y = \frac{1}{4}
\
