Question

simplify.
\frac{6w^{2}}{36w^{5}}

Explanation:

Step1: Simplify the coefficients

Simplify the fraction of the coefficients \( \frac{6}{36} \). We can divide both the numerator and the denominator by their greatest common divisor, which is 6. So, \( \frac{6\div6}{36\div6}=\frac{1}{6} \).

Step2: Simplify the variables using exponent rules

For the variable \( w \), we use the rule of exponents \( \frac{a^m}{a^n}=a^{m - n} \) (where \( a
eq0 \), \( m \) and \( n \) are real numbers). Here, \( m = 2 \) and \( n = 5 \), so \( \frac{w^{2}}{w^{5}}=w^{2-5}=w^{-3} \). And we know that \( w^{-3}=\frac{1}{w^{3}} \) (by the definition of negative exponents \( a^{-n}=\frac{1}{a^{n}} \) for \( a
eq0 \) and \( n \) a positive integer).

Step3: Combine the simplified coefficient and variable

Multiply the simplified coefficient and the simplified variable part. So we have \( \frac{1}{6}\times\frac{1}{w^{3}}=\frac{1}{6w^{3}} \).

Answer:

\( \frac{1}{6w^{3}} \)