Question

solve. write your answer as an integer or a fraction in simplest form.
$256^{x + 1} = 16$
$x = $

Explanation:

Step1: Express bases as powers of 16

$256 = 16^2$, so rewrite the equation:
$$16^{2(x+1)} = 16^1$$

Step2: Set exponents equal (same base)

Since bases are equal, exponents are equal:
$$2(x+1) = 1$$

Step3: Solve for x

Expand and isolate x:
$$2x + 2 = 1$$
$$2x = 1 - 2$$
$$2x = -1$$
$$x = \frac{-1}{2}$$

Answer:

$\boldsymbol{-\frac{1}{2}}$