\((\dfrac{1}{2})^{15}\times(\dfrac{1}{2})^{20}=(\dfrac{1}{2})^{15+20}=(\dfrac{1}{2})^{35}\) \([(\dfrac{1}{3})^2]^{25}\div(\dfrac{1}{3})^{30}=(\dfrac{1}{3})^{50}\div(\dfrac{1}{3})^{30}=(\dfrac{1}{3})^{50-30}=(\dfrac{1}{3})^{20}\) \((\dfrac{1}{16})^3\div(\dfrac{1}{8})^2=[(\dfrac{1}{2})^4]^3\div[(\dfrac{1}{2})^3]^2=(\dfrac{1}{2})^{12}\div(\dfrac{1}{2})^6=(\dfrac{1}{2})^{12-6}=(\dfrac{1}{2})^6\) (x^3)^2 : ( x^2)^3= x^6 :x^6=1
\(\left(\dfrac{1}{2}\right)^{15}.\left(\dfrac{1}{2}\right)^{20}=\left(\dfrac{1}{2}\right)^{15+20}=\left(\dfrac{1}{2}\right)^{35}\)
\(\left(\dfrac{1}{9}\right)^{25}:\left(\dfrac{1}{3}\right)^{30}=\left[\left(\dfrac{1}{3}\right)^2\right]^{25}:\left(\dfrac{1}{3}\right)^{30}=\left(\dfrac{1}{3}\right)^{50}:\left(\dfrac{1}{3}\right)^{30}=\left(\dfrac{1}{3}\right)^{50-30}=\left(\dfrac{1}{30}\right)^{20}\)\(\left(\dfrac{1}{16}\right)^3:\left(\dfrac{1}{8}\right)^2=\left[\left(\dfrac{1}{2}\right)^4\right]^3:\left[\left(\dfrac{1}{2}\right)^3\right]^2=\left(\dfrac{1}{2}\right)^{12}:\left(\dfrac{1}{2}\right)^6=\left(\dfrac{1}{2}\right)^{12-6}=\left(\dfrac{1}{2}\right)^6\)
\(\left(x^3\right)^2:\left(x^2\right)^3=x^6:x^6=x^0=1\)
