Question

multiply the following rational expressions. write the answer in lowest terms.
$\frac{6y^{6}}{5}cdot\frac{10}{21y}$
$\frac{6y^{6}}{5}cdot\frac{10}{21y}=square$
(simplify your answer. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Multiply numerators and denominators

$\frac{6y^{6}}{5}\cdot\frac{10}{21y}=\frac{6y^{6}\times10}{5\times21y}$

Step2: Simplify the numerical part

$6\times10 = 60$ and $5\times21=105$, so we have $\frac{60y^{6}}{105y}$

Step3: Use exponent - rule for $y$ terms

$\frac{y^{6}}{y}=y^{6 - 1}=y^{5}$, so the expression becomes $\frac{60y^{5}}{105}$

Step4: Simplify the fraction

Find the greatest common divisor of 60 and 105. GCD(60, 105)=15. Divide both numerator and denominator by 15: $\frac{60\div15}{105\div15}y^{5}=\frac{4y^{5}}{7}$

Answer:

$\frac{4y^{5}}{7}$