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