Question

select the correct answer. solve the exponential equation for x. $256 = \left(\frac{1}{4}\
ight)^{3x + 2}$ a. $x = -2$ b. $x = 2$ c. $x = 4$ d. $x = -4$

Explanation:

Step1: Rewrite bases as powers of 4

$256 = 4^4$, $\frac{1}{4}=4^{-1}$, so:
$4^4 = (4^{-1})^{3x+2}$

Step2: Simplify right-hand side

Use exponent rule $(a^m)^n=a^{m \cdot n}$:
$4^4 = 4^{-(3x+2)}$

Step3: Equate exponents (same base)

Since bases are equal, exponents are equal:
$4 = -(3x+2)$

Step4: Solve for x

First expand the right side:
$4 = -3x - 2$
Add 2 to both sides:
$4+2 = -3x$
$6 = -3x$
Divide by -3:
$x = \frac{6}{-3} = -2$

Answer:

A. $x = -2$