[tex]\begin{gathered} 4^3\times4^{-6}=4^5\times4^{\text{?}} \\ 4^{(3-6)}=4^5\times4^? \\ \frac{4^{-3}}{4^5}=4^? \\ 4^{(-3-5)}=4^{\text{?}} \\ 4^{-8}=4^{\text{?}} \\ \text{Thus, the exponent is -8.} \end{gathered}[/tex][tex]\begin{gathered} (5^{-3})^2=(5^{-6})^{\text{?}} \\ 5^{-6}=5^{-6?} \\ \text{Take log of both side}, \\ -6\log \text{ 5=-6?log 5} \\ -6=-6 \\ So,\text{ the exponent is 1.} \end{gathered}[/tex]
