Evaluate the Function y=2(4)^x , x=-2

$y = 2 {(4)}^{x}$ , $x = - 2$

Replace all occurrences of $x$ with $- 2$ in each equation.

Replace all occurrences of $x$ in $y = 2^{1 + 2 x}$ with $- 2$ .

$y = 2^{1 + 2 (- 2)}$

$x = - 2$

Simplify the right side.

Simplify $2^{1 + 2 (- 2)}$ .

Multiply $2$ by $- 2$ .

$y = 2^{1 - 4}$

$x = - 2$

Subtract $4$ from $1$ .

$y = 2^{- 3}$

$x = - 2$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$y = \frac{1}{2^{3}}$

$x = - 2$

Raise $2$ to the power of $3$ .

$y = \frac{1}{8}$

$x = - 2$

$y = \frac{1}{8}$

$x = - 2$

$y = \frac{1}{8}$

$x = - 2$

$y = \frac{1}{8}$

$x = - 2$

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(- 2, \frac{1}{8})$

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