Question

4 what value of n makes the equation true? show your work.
a. $13^{-n} = \frac{1}{13^{-3}}$
solution

Explanation:

Step1: Simplify the right - hand side using the negative exponent rule

The negative exponent rule states that $\frac{1}{a^{-m}}=a^{m}$. For the right - hand side of the equation $13^{-n}=\frac{1}{13^{-3}}$, applying this rule, we get $\frac{1}{13^{-3}} = 13^{3}$. So the equation becomes $13^{-n}=13^{3}$.

Step2: Use the property of exponential functions with the same base

If $a^{x}=a^{y}$ (where $a>0,a
eq1$), then $x = y$. Since the base $a = 13$ is the same on both sides of the equation $13^{-n}=13^{3}$, we can set the exponents equal to each other. That is, $-n=3$.

Step3: Solve for n

To solve for $n$, we multiply both sides of the equation $-n = 3$ by $- 1$. So $n=-3$.

Answer:

$n = - 3$