remember
try and group like bases
and
(x^m)(x^n)=x^(m+n)
also
x^0=1
and
(ab)/(cd)=(a/c)(b/d)
and
(x^m)/(x^n)=x^(m-n)
and
x^-m=1/(x^m)
\(\frac{(4^{3})(4^{-1})(5^{-2})}{(4^{4})(5^{-3})((-3)^{0})}\)
simplify a few stuff
on top
(4^3)(4^-1)=4^(3-1)=4^2
on bottom
(-3)^0=1
which cancels out since 1 times x=x so disregard the (-3)^0
now we have
\(\frac{(4^{2})(5^{-2})}{(4^{4})(5^{-3})}\)
split into 2 fractions with 4's in one and 5's in other
(\(\frac{4^{2}}{4^{4}}\))(\(\frac{5^{-2}}{5^{-3}}\))
remember the exponential law
first fraction
\(\frac{4^{2}}{4^{4}}\)=4^(2-4)=4^-2
second
(\(\frac{5^{-2}}{5^{-3}}\))=5^(-2-(-3))=5^(-2+3)=5^1=5
now we have
(4^-2)(5)=(1/(4^2))(5)=5/(4^2)=5/16
