## Precalculus (6th Edition)

False Correct Statement: $m^{2/3} \cdot m^{1/3} = m$
RECALL: (1) $a^{-m} = \dfrac{1}{a^m}$ (2) $\dfrac{a^m}{a^n} = a^{m-n}$ (3) $a^1=a$ (4) $a^m\cdot a^n = a^{m+n}$ Use rule (4) above to obtain: $m^{2/3} \cdot m^{1/3}=m^{2/3+1/3}=m^1=m$ Thus, the given statement is false. The correct statement is: $m^{2/1} \cdot m^{1/3} = m$