Questions: Simplify. 36x^4 / 63x^6

Solution Steps

The given expression is

\[ \frac{36 x^{4}}{63 x^{6}} \]

First, simplify the coefficients \( \frac{36}{63} \). The greatest common divisor (GCD) of 36 and 63 is 9. Therefore, divide both the numerator and the denominator by 9:

\[ \frac{36}{63} = \frac{36 \div 9}{63 \div 9} = \frac{4}{7} \]

Next, simplify the variable part \( \frac{x^4}{x^6} \). Use the property of exponents that states \( \frac{x^a}{x^b} = x^{a-b} \):

\[ \frac{x^4}{x^6} = x^{4-6} = x^{-2} \]

Combine the simplified coefficient and variable parts:

\[ \frac{4}{7} \cdot x^{-2} = \frac{4}{7x^2} \]

Final Answer