# Thread: NEED HELP having trouble with negative exponents and variables

1. ## NEED HELP having trouble with negative exponents and variables

-3((b)^-2)+6=-6 I can find the answer on an online calculator but i would very much like to know how to do find b via step by step

2. ## Re: NEED HELP having trouble with negative exponents and variables

$-3b^{-2}+6=-6$

Use SAMDEB (Subtraction/Addition, Multiplication/Division, Exponents, Brackets, Repeat if necessary after brackets removed)

In this case
$-3b^{-2}= -12$ subtract 6 on both sides
$b^{-2} = 4$ divide by -3 on both sides
$b^{2} = \frac{1}{4}$ Multiply both sides by b^{-2} and divide by 4
$b = \sqrt{\frac{1}{4}$ Take the square root on both sides (Exponents)
$b = \frac{1}{2}$ Recall the fact that since the square root is also a power (of $\frac{1}{2}$) and hence $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$