Question 72989
{{{(-1/5)^3((-1/3)^2 + (1/12)*(1/6 - (-1/4)^3))}}}Start with given expression
{{{((-1)^3/5^3)(((-1)^2/3^2) + (1/12)*(1/6 - ((-1)^3/4^3)))}}}Distribute the exponents to both numerators and denominators with exponents
Any negative number raised to a odd power  will have a negative sign (ie {{{(-1)^3=-1}}}) and any negative number raised to a even power will have a positive sign ie ({{{(-1)^4=1}}}).
{{{((-1)/125)((1/9) + (1/12)*(1/6 - ((-1)/64)))}}}Simplify the exponents
{{{((-1)/125)(1/9 + 1/72 + 1/768))}}}Distribute the 1/12
{{{((-1)/125)((256+32+3)/2304))}}} Add the values in the parenthesis (I found the LCD of 2304 and added the corresponding numerators)
{{{((-1)/125)((291)/2304))}}}Multiply the fractions
{{{((-291)/288000))}}}Simplify
{{{-97/96000=-0.00101041666}}}Approximately note: the last group of 6's repeat forever.
Hope that helps. I know there are a lot of steps that I glossed over (I'm assuming you have adequate knowledge of order of operations, exponents, fractions, etc.), so ask about any step I explained.