these just teest your understanding or memory on the exponential rules
the rules for each are as follows
a. [tex](x^m)(x^n)=x^{m+n}[/tex]
b. [tex] \frac{x^m}{x^n}=x^{m-n} [/tex]
c. [tex]x^{-m}= \frac{1}{x^m} [/tex]
d. [tex](ab)^m=(a^m)(b^m)[/tex] and [tex](x^m)^n=x^{mn}[/tex]
so
a. [tex](x^3)(x^{-2})=x^{3-2}=x^{1}=x[/tex]
b. [tex] \frac{y^5}{y^{-2}}=y^{5-(-2)}=y^{5+2}=y^{7} [/tex]
c. [tex]4^{-1}= \frac{1}{4^1}= \frac{1}{4} [/tex]
d. [tex](4x^2)^3=(4^3)((x^2)^3)[/tex] and [tex](x^2)^3=x^{2*3}=x^{6}[/tex]
result is[tex]64x^6[/tex]
