Question

4(3xy^4)^3/(2x^3y^5)^4

Answer 1

Answer:

$\frac{4\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}=\frac{27}{4x^9y^8}$

Step-by-step explanation:

Given the expression

$\:\:\frac{4\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}$

solving the expression

$\:\:\frac{4\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}=4\cdot \:\frac{\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}$

             $=4\:\frac{27x^3y^{12}}{16x^{12}y^{20}}$

              $=4\cdot \frac{3^3}{2^4x^9y^8}$

The multiply fractions are defined as

$\:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}$

so the expression becomes

                $=\frac{3^3\cdot \:4}{2^4x^9y^8}$

                $=\frac{3^3\cdot \:2^2}{2^4x^9y^8}$

                $=\frac{3^3}{2^2x^9y^8}$

Refining

                 $=\frac{27}{4x^9y^8}$

Therefore,

$\frac{4\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}=\frac{27}{4x^9y^8}$