Question 889421: What is (6m^4*n)/(2n^3*m^6)? Its got something to do with negative indices cuz the book says so, but I don't see anything...? Found 2 solutions by rothauserc, Edwin McCravy:Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! (6m^4*n)/(2n^3*m^6)
when we have an exponent raised to another exponent we multiply the exponents, therefore
(6m^4*n)/(2n^3*m^6) = 6m^4n / 2n^18m
divide numerator and denominator by 2
(6m^4*n)/(2n^3*m^6) = 3m^4n / n^18m
now 1/n^18m = n^-18m, therefore
(6m^4*n)/(2n^3*m^6) = 3m^4n * n^-18m
The other answer given is incorrect.
Think of it this way and you don't have to deal with negative exponents:
Write 6 as 2×3
Write m4 as m×m×m×m
Write n3 as n×n×n
Write m6 as m×m×m×m×m×m
The shortcut rule is:
Subtract the exponents of like bases, largest minus smallest, and put
the result in the numerator or denominator depending on where the
larger exponent was. In this case the larger exponents of both letters
were in the denominator, so when you subtract the exponents 3-1=2 and
6-4=2, you put both 2 exponents of n and m in the denominator.
Edwin
