Question

simplify.
\frac{11^{3} 11^{4}}{11^{2} 11^{6}}

Explanation:

Step1: Use exponent rule for division

When dividing terms with the same base, we subtract the exponents. For the base \( n \), the numerator has exponents \( 3 \) and \( 4 \) (wait, actually, let's re - express the given expression. The expression is \( \frac{n^{3}n^{4}}{n^{2}n^{6}} \). First, use the product rule of exponents \( a^{m}\times a^{n}=a^{m + n} \) for numerator and denominator separately.

For the numerator: \( n^{3}\times n^{4}=n^{3 + 4}=n^{7} \)

For the denominator: \( n^{2}\times n^{6}=n^{2+6}=n^{8} \)

Step2: Apply division rule of exponents

Now we have \( \frac{n^{7}}{n^{8}} \). Using the rule \( \frac{a^{m}}{a^{n}}=a^{m - n} \) (where \( a=n \), \( m = 7 \), \( n = 8 \)), we get \( n^{7-8}=n^{- 1} \) or \( \frac{1}{n} \)

Answer:

\( \frac{1}{n} \) (or \( n^{-1} \))