Question

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

Answer 1

See a solution process below:

Explanation:

First, simplify all the individual exponent terms using this rule of exponents:

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

`(4(x^color(red)(2))^color(blue)(3)(y^color(red)(4))^color(blue)(2))/(2(x^color(red)(2))^color(blue)(2)(y^color(red)(2))^color(blue)(4)) => (4x^(color(red)(2) xx color(blue)(3))y^(color(red)(4) xx color(blue)(2)))/(2x^(color(red)(2) xx color(blue)(2))y^(color(red)(2) xx color(blue)(4))) = (4x^6y^8)/(2x^4y^8)`

We can now rewrite this expression as:

`4/2(x^6/x^4)(y^8/y^8) => 2(x^6/x^4)1 => 2(x^6/x^4)`

We can now use this rule of exponents to complete the simplification of the `x` terms:

`x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))`

`2(x^color(red)(6)/x^color(blue)(4)) => 2x^(color(red)(6)-color(blue)(4)) =>`

`2x^2`