Question

Only 100 points for you to answer to my math word problem question but please don’t post a very useless answer on The Brainly! >:(
Consider the following expression that looks like this:$\frac{3x^{3}y*6xy^{3}}{(-3xy)^{2}}.$

What can you describe the advantages and the disadvantages of each method?

Please help me as soon as possible will get the brainliest award if your answers are the best step-by-step explanations and an efforts into it, well anyways, good luck on answering the math word problem question of my last year’s math word problem homework from The Hung Vuong Learning Centre Incorporated, and I will be there checking the answers to see if it’s appropriate. :)

Answer 1

We need to simplify it

$\\ \tt\longmapsto \dfrac{3x^36xy^3}{(-3xy)^2}$

Apply

• (ab)^n=a^nb^n
• a^n+a^m=a^m+n

$\\ \tt\longmapsto \dfrac{18x{3+1}y^{1+3}}{9x^2y^2}$

$\\ \tt\longmapsto \dfrac{18x^4y^4}{9x^2y^2}$

• a^m/a^n=a^m-n

$\\ \tt\longmapsto 2x^2y^2$

hope it helps

Answer 2

Answer:

$\dfrac{3x^3y*6xy^3}{(-3xy)^2}=2x^2y^2$

Step-by-step explanation:

$\dfrac{3x^3y*6xy^3}{(-3xy)^2}$

Numerator

Multiply the constants, and apply the exponent rule: $a^b\cdot \:a^c=a^{b+c}$

$3x^3y*6xy^3=(3*6)x^{(3+1)}y^{(1+3)}=18x^4y^4$

Denominator

Apply the exponent rule:  $\left(-a\right)^n=a^n,\:\quad \mathrm{if\:}n\mathrm{\:is\:even}$

$(-3xy)^2=(3xy)^2$

Apply the exponent rule:  $\quad \left(a\cdot \:b\right)^n=a^nb^n$

$(3xy)^2=3^2x^2y^2=9x^2y^2$

Therefore,

$\dfrac{3x^3y*6xy^3}{(-3xy)^2}=\dfrac{18x^4y^4}{9x^2y^2}$

Factor 18 and cancel the common factor 9:

$\implies \dfrac{18x^4y^4}{9x^2y^2}=\dfrac{9*2x^4y^4}{9x^2y^2}\\\\\\\implies \dfrac{9*2x^4y^4}{9x^2y^2}=\dfrac{2x^4y^4}{x^2y^2}$

Apply the exponent rule: $\dfrac{x^a}{x^b}=x^{a-b}$

$\implies \dfrac{2x^4y^4}{x^2y^2}=2x^2y^2$