Chapter 4 - Section 4.1 - Integer Exponents and Scientific Notation - 4.1 Exercises: 71

$\frac{1}{6^{10}}$

Work Step by Step

According to the quotient rule for exponents, $\frac{a^{m}}{a^{n}}=a^{m-n}$ (where $a\ne0$). Therefore, $\frac{6^{-3}}{6^{7}}=6^{-3-7}=6^{-10}$. Furthermore, the definition of negative exponents tells us that $a^{-n}=\frac{1}{a^{n}}$. Therefore, $6^{-10}=\frac{1}{6^{10}}$.

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