Question

How do you simplify `x^ { 3} y ^ { 2} z ^ { 2} \cdot x ^ { 2} y ^ { 3} z ^ { 4} \cdot x ^ { 3} y ^ { 2}`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(x^3 * x^2 * x^3)(y^2 * y^3 * y^2)(z^2 * z^4)`

Now, we can use this rule of exponents to simplify the individual variables:

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

`(x^color(red)(3) * x^color(blue)(2) * x^color(green)(3))(y^color(red)(2) * y^color(blue)(3) * y^color(green)(2))(z^color(red)(2) * z^color(blue)(4)) =>`

`x^(color(red)(3)+color(blue)(2)+color(green)(3))y^(color(red)(2)+color(blue)(3)+color(green)(2))z^(color(red)(2)+color(blue)(4)) =>`

`x^8y^7z^6`