Question

How do you multiply `2x ^ { 4} \cdot ( x ^ { 3} y ^ { 2} ) ^ { 3}`?

Answer 1

See a solution process below:

Explanation:

First, expand the terms within parenthesis using this rule for exponents:

`(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))`

`2x^4 * (x^color(red)(3)y^color(red)(2))^color(blue)(3) = 2x^4 * x^(color(red)(3) xx color(blue)(3))y^(color(red)(2) xx color(blue)(3)) = 2x^4 * x^9y^6`

Next, rewrite the expression as:

`2x^4 * x^9y^6 = 2y^6 * x^4x^9`

Now, use this rule of exponents to multiply the `x` terms and complete the simplification:

`x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))`

`2y^6 * x^color(red)(4)x^color(blue)(9) = 2y^6 * x^(color(red)(4) + color(blue)(9)) = 2y^6 * x^13 = 2x^13y^6`

Answer 2

`2x^13y^6`

Explanation:

Begin by distributing the exponent:

`(x^3y^2)^3 = (x^(3*3)y^(2*3)) = (x^9y^6)`

We now have:

`2x^4(x^9y^6)`

Apply the exponent rule: `a^b*a^c=a^(b+c)` to the `x^4` and `x^9`

`2x^13y^6`