Question

module 2 practice test
score: 2/16 answered: 2/16
question 5
multiply. write your answer in lowest terms.
$\frac{2y^{13}w^{5}}{5y^{5}}cdot\frac{1w^{2}}{12y^{5}w^{3}}$

Explanation:

Step1: Multiply numerators and denominators

Multiply the numerators together: $(2y^{13}w^{5})\times(1w^{2}) = 2y^{13}w^{7}$. Multiply the denominators together: $(5y^{5})\times(12y^{5}w^{3})=60y^{10}w^{3}$. So the expression becomes $\frac{2y^{13}w^{7}}{60y^{10}w^{3}}$.

Step2: Simplify coefficients and use exponent - rules

Simplify the coefficient $\frac{2}{60}=\frac{1}{30}$. For the variables with the same base, use the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$. For $y$, we have $y^{13-10}=y^{3}$, and for $w$, we have $w^{7 - 3}=w^{4}$.

Answer:

$\frac{y^{3}w^{4}}{30}$