Simplify {(1/3)^-2 -(1/2)^-2 } / (1/4)^-2

-20/9

Step-by-step explanation:

you need to know that terms with negative exponents go into the denominator and then the exponent becomes positive

you also need to remember that, when dividing fractions, you multiply by the reciprocal

example:  ()^-3 = 1/125

{(1/3)^-2 -(1/2)^-2 } / (1/4)^-2

simplify terms, one at a time:

(1/3)^-2  = (1/3)^2 = 1/9

(1/2)^-2  = (1/2)^2 = 1/4

(1/4)^-2 = (1/4)^2 =  1/16  

1/9 - 1/4 = 4/36 - 9/36 = -5/36

-5/36 ÷ 1/16 =  -5/36 · 16/1  =  -20/9

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^