color(red)("How you would normally see the calculation")
variants on:
color(red)(-(2xx5)(a^(7-2)) = -10a^5)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(green)("Very detailed solution split into 3 parts")
Part 1 -> signs
Part 2 -> numbers
Part 3 -> the letters (variables)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Part 1 "-> " signs")
Write the signs as -1 and +1" " ( this does work!)
The signs are not the same as each other so
(-1)xx(+1) = color(red)((-1))
color(blue)("So our answer is a negative value ")
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Part 2 "-> " numbers")
2xx5 =color(red)(10)
color(blue)("The number part of the answer is 10")
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Part 3 "-> " letters (variables)")
We have:" "a^7xxa^(-2)
color(brown)("Shortcut method")
Because the letters (variables) are the same we can do this:
a^7xxa^(-2)" "=" "a^(7-2)" "=color(red)(a^5)
'......................................................
color(brown)("First principles method")
a^(-2)" is the same thing as "1/a^2
So::" "a^7xxa^(-2)" " =" " a^7xx1/a^2
Let a^7 be written as a^5xxa^2
Then we have: a^5xxa^2xx1/a^2
This is the same as
" "a^5xxa^2/a^2
But a^2/a^2=1
" "a^5xxa^2/a^2" "=" "color(red)(a^5)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("putting it all together")
color(red)((-2a^7)(5a^(-2))= -10a^5)
