Question

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

Answer 1

You should use order of operations to simplify the equation. Here's the math:

$4(3x^2y^4)^3 / (2x^3y^5)^4$ 

Let's work on one equation at a time, first this one: 

$4(3x^2y^4)^3$

Distribute the exponent (³) to all the terms within the parentheses:

$4(3^3x^2x^3y^4y^3)$

Remember to multiply the exponents for variables. Now, simplify the terms:

$4(27x^6y^1^2)$

Distribute $4$ to all the terms in parentheses:

$108x^64y^1^2$

Now, let's work on the second expression: 

$(2x^3y^5)^4$

First, distribute the exponent $(^4)$ to the terms in parentheses:

$(2^4x^3x^4y^5y^4)$

Simplify by multiplying the exponents:

$(16x^1^2y^2^0)$

Now, we can find the quotient of the two expressions:

$\frac{(108x^64y^1^2)}{(16x^1^2y^2^0)}$

Separate the $x$ terms in the denominator into factors that go into the numerator:

$\frac{(108x^64y^1^2)}{(4x^64x^2y^2^0)}$

Divide:

$\frac{27(4y^1^2)}{4x^2y^2^0}$

Distribute $27$:

$\frac{108y^1^2}{4x^2y^2^0}$

Separate the $y$ terms in the denominator into factors that go into the numerator:

$\frac{108y^1^2}{4x^2y^4y^5}$

Divide:

$\frac{108y^3}{4x^2y^5}$

Simplify:

$\frac{27}{4x^6y^8}$

Hope this helps!

Answer 2

3/4x^10y^16 should be the answer if my math is correct.