Question

type the correct answer in the box. use numbers instead of words. what value of y makes the equation true? $25^{y + 1}=\frac{1}{5^{4 - y}}$ y =

Explanation:

Step1: Rewrite base 25 as $5^2$

$5^{2(y+1)} = \frac{1}{5^{4-y}}$

Step2: Rewrite right side with negative exponent

$5^{2(y+1)} = 5^{-(4-y)}$

Step3: Equate exponents (same base)

$2(y+1) = -(4-y)$

Step4: Expand both sides

$2y + 2 = -4 + y$

Step5: Solve for y

$2y - y = -4 - 2$
$y = -6$

Answer:

$-6$