Question

simplify.
\frac{56w^{3}}{49w^{4}}

Explanation:

Step1: Simplify the coefficients

First, find the greatest common divisor (GCD) of 56 and 49. The GCD of 56 and 49 is 7. Divide both the numerator and the denominator by 7:
$\frac{56\div7}{49\div7} = \frac{8}{7}$

Step2: Simplify the variable terms

For the variable $w$, use the quotient rule of exponents: $a^m\div a^n = a^{m - n}$. Here, $m = 3$ and $n = 4$, so $w^3\div w^4 = w^{3 - 4} = w^{-1}=\frac{1}{w}$

Step3: Multiply the simplified coefficient and variable terms

Multiply the results from Step 1 and Step 2:
$\frac{8}{7}\times\frac{1}{w}=\frac{8}{7w}$

Answer:

$\frac{8}{7w}$