Question

Solve the following problem:

Answer 1

Answer:

$n^{8}$

Step-by-step explanation:

Given the Quotient Rule of Exponents: $\frac{a^{m}}{a^{n}} = a^{(m-n)}$, you must subtract the exponents of each exponential expression (in fractions) before applying the Product Rule of Exponents (I will explain in a while what it means).

First, subtract the exponents of the first fraction, $\frac{n^{5}}{n^{3}} = n^{(5 - 3)} = n^{2}$

Next, subtract the exponents of the second fraction:  $\frac{n^{9}}{n^{3}} = n^{(9 - 3)} = n^{6}$

At this point, we have the following exponential expressions: $n^{2}$ and $n^{6}$.

Since the required operation is multiplication, then you can apply the Product Rule of Exponents: $a^{m} a^{n} = a^{(m+n)}$

$n^{2}*n^{6} = n^{(2+6)} = n^{8}$

Therefore, the correct answer is $n^{8}$.

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