which statement is true?\na $\frac{6^{-14}}{6^{-13}}<(6^{-13})cdot(6^{-12})$\nb $\frac{6^{-14}}{6^{-13}}>(6^{…

which statement is true?\na $\frac{6^{-14}}{6^{-13}}<(6^{-13})cdot(6^{-12})$\nb $\frac{6^{-14}}{6^{-13}}>(6^{-13})cdot(6^{-12})$\nc $\frac{6^{-14}}{6^{-13}}=(6^{-13})cdot(6^{-12})$

which statement is true?\na $\frac{6^{-14}}{6^{-13}}<(6^{-13})cdot(6^{-12})$\nb $\frac{6^{-14}}{6^{-13}}>(6^{-13})cdot(6^{-12})$\nc $\frac{6^{-14}}{6^{-13}}=(6^{-13})cdot(6^{-12})$

Answer

Explanation:

Step1: Simplify the left - hand side

Use the quotient rule of exponents $\frac{a^m}{a^n}=a^{m - n}$. For $\frac{6^{-14}}{6^{-13}}$, we have $6^{-14-(-13)}=6^{-14 + 13}=6^{-1}=\frac{1}{6}$.

Step2: Simplify the right - hand side

Use the product rule of exponents $a^m\cdot a^n=a^{m + n}$. For $(6^{-13})\cdot(6^{-12})$, we get $6^{-13+( - 12)}=6^{-25}=\frac{1}{6^{25}}$.

Step3: Compare the two results

Since $\frac{1}{6}>\frac{1}{6^{25}}$ (when the numerators are the same, the fraction with the smaller denominator is larger), so $\frac{6^{-14}}{6^{-13}}>(6^{-13})\cdot(6^{-12})$.

Answer:

B. $\frac{6^{-14}}{6^{-13}}>(6^{-13})\cdot(6^{-12})$