which statement is true?\na $(6^{4})^{-5}<(6^{-7})cdot(6^{-3})$\nb $(6^{4})^{-5}>(6^{-7})cdot(6^{-3})$\nc…

which statement is true?\na $(6^{4})^{-5}<(6^{-7})cdot(6^{-3})$\nb $(6^{4})^{-5}>(6^{-7})cdot(6^{-3})$\nc $(6^{4})^{-5}=(6^{-7})cdot(6^{-3})$

which statement is true?\na $(6^{4})^{-5}<(6^{-7})cdot(6^{-3})$\nb $(6^{4})^{-5}>(6^{-7})cdot(6^{-3})$\nc $(6^{4})^{-5}=(6^{-7})cdot(6^{-3})$

Answer

Explanation:

Step1: Simplify the left - hand side

Use the power - of - a - power rule $(a^m)^n=a^{mn}$. For $(6^{4})^{-5}$, we have $6^{4\times(-5)} = 6^{-20}$.

Step2: Simplify the right - hand side

Use the product rule $a^m\times a^n=a^{m + n}$. For $(6^{-7})\times(6^{-3})$, we get $6^{-7+( - 3)}=6^{-10}$.

Step3: Compare the two results

Since when the base $a = 6>1$ and the exponents are negative, and $-20<-10$, we know that $6^{-20}<6^{-10}$. That is, $(6^{4})^{-5}<(6^{-7})\times(6^{-3})$.

Answer:

A. $(6^{4})^{-5}<(6^{-7})\cdot(6^{-3})$