Question

solve. write your answer as an integer or a fraction in simplest form.
$4 = 16^{4x}$
$x = \square$
submit

Explanation:

Step1: Rewrite bases as powers of 2

$4 = 2^2$, $16 = 2^4$, so:
$2^2 = (2^4)^{4x}$

Step2: Simplify right-hand side

Use exponent rule $(a^m)^n = a^{mn}$:
$2^2 = 2^{16x}$

Step3: Equate exponents (same base)

Set exponents equal since bases are equal:
$2 = 16x$

Step4: Solve for x

Divide both sides by 16:
$x = \frac{2}{16} = \frac{1}{8}$

Answer:

$\frac{1}{8}$