Question

8.6 solve radical equations (homework)
score: 14/16 answered: 14/16
question 15
solve.
(9b - 4)^(1/4) - 6 = -3
b =

Explanation:

Step1: Isolate the radical term

Add 6 to both sides of the equation $(9b - 4)^{\frac{1}{4}}-6=-3$.
$(9b - 4)^{\frac{1}{4}}=-3 + 6$
$(9b - 4)^{\frac{1}{4}}=3$

Step2: Eliminate the fourth - root

Raise both sides of the equation to the fourth power.
$((9b - 4)^{\frac{1}{4}})^4=3^4$
Using the power - of - a - power rule $(a^m)^n=a^{mn}$, we have $9b-4 = 81$.

Step3: Solve for b

Add 4 to both sides of the equation: $9b=81 + 4$, so $9b=85$.
Then divide both sides by 9: $b=\frac{85}{9}$.

Answer:

$\frac{85}{9}$