Question

simplify to lowest terms, if possible: $\frac{6m^{2}y^{5}}{10y^{4}m^{2}}$ question help: video add work

Explanation:

Step1: Divide the coefficients

Divide 10 by 6. $\frac{10}{6}=\frac{5}{3}$.

Step2: Apply the quotient - rule of exponents for $m$

For the $m$ terms, $\frac{m^{2}}{m^{2}}=m^{2 - 2}=m^{0}=1$ (using the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$).

Step3: Apply the quotient - rule of exponents for $y$

For the $y$ terms, $\frac{y^{4}}{y^{5}}=y^{4-5}=y^{-1}=\frac{1}{y}$ (using the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$).

Step4: Combine the results

Multiply the results from the previous steps: $\frac{5}{3}\times1\times\frac{1}{y}=\frac{5}{3y}$.

Answer:

$\frac{5}{3y}$