Questions: Simplify the expression. 7^-14 / 7 7^-14 / 7 = (Simplify your answer. Type exponential notation with positive exponents.)

Transcript text: Simplify the expression. \[ \begin{array}{c} \frac{7^{-14}}{7} \\ \frac{7^{-14}}{7}= \end{array} \] $\square$ (Simplify your answer. Type exponential notation with positive exponents.)

Solution

Solution Steps

To simplify the expression $\frac{7^{-14}}{7}$, we can use the properties of exponents. Specifically, we can use the rule that $\frac{a^m}{a^n} = a^{m-n}$. Here, $a = 7$, $m = -14$, and $n = 1$.

Step 1: Apply the Property of Exponents

To simplify the expression $\frac{7^{-14}}{7}$, we use the property of exponents: \[ \frac{a^m}{a^n} = a^{m-n} \] Here, $a = 7$, $m = -14$, and $n = 1$.

Step 2: Subtract the Exponents

Using the property, we subtract the exponents: \[ 7^{-14 - 1} = 7^{-15} \]