Question

cphs : advanced algebra: concepts and connections - block (27.0831030)
negative exponents
reviewing laws of exponents
write the expression using a single exponent.
\\( \frac{5^9}{5^{13}} = 5^a \\)
\\( a = \square \\)

Explanation:

Step1: Recall the exponent rule for division

When dividing two numbers with the same base, we subtract the exponents: $\frac{b^m}{b^n}=b^{m - n}$. Here, the base $b = 5$, $m = 2$, and $n = 3$.

Step2: Apply the rule to $\frac{5^2}{5^3}$

Using the rule $\frac{5^2}{5^3}=5^{2 - 3}$.

Step3: Calculate the exponent

Simplify $2 - 3=-1$. So, $a=-1$.

Answer:

-1