Math Snap

STEP 1

1. We are asked to simplify the given expression.
2. The expression involves division of monomials.
3. Simplification involves reducing coefficients and applying the laws of exponents.

STEP 2

1. Simplify the coefficients in the fraction.
2. Apply the laws of exponents to simplify the variable terms.

STEP 3

Identify the coefficients in the fraction $\frac{8}{48}$ and simplify them by finding the greatest common divisor (GCD).
The GCD of 8 and 48 is 8. Therefore, simplify the fraction:
$$\frac{8}{48} = \frac{8 \div 8}{48 \div 8} = \frac{1}{6}$$

STEP 4

Apply the laws of exponents to simplify the variable terms $\frac{u^{2}}{u^{5}}$.
According to the laws of exponents, $\frac{u^{a}}{u^{b}} = u^{a-b}$.
$$\frac{u^{2}}{u^{5}} = u^{2-5} = u^{-3}$$

Combine the simplified coefficient and the simplified variable term:
$$\frac{1}{6} \times u^{-3} = \frac{1}{6u^{3}}$$ The simplified expression is:
$$\boxed{\frac{1}{6u^{3}}}$$