Question

Simplify the given expression. Assume that no variable equals 0. (14x20y10 / 28x12y14)4

Answer 1

`(1)/(43904x^(28)y^(46))`

Explanation:

Simplify:

`(14x^(20)y^(10))/((28x^(12)y^(14))^4)`

Use this property in the denominator:

`(x^y)^z=x^(yz)`

And multiply each exponent in the denominator by 4:

`(14x^(20)y^(10))/((28^4x^(48)y^(56)))`

Use these properties:

`x^(-n)=(1)/(x^n)`

`x^yx^z=x^(y+z)`

And combine powers:

`(14x^(20-48)y^(10-56))/(28^4) =(14x^(-28) y^(-46))/(28^4) =(14)/(28^4 x^(28) y^(46))`

Divide the constants:

`(14)/(28^4) =(14)/(614656) =(1)/(43904)`

Therefore, the simplied expression is:

`(1)/(43904x^(28)y^(46))`

Answer 2

`(1)/(2^(4)*14^(3) *x^(28)*y^(46))`

Explanation:

To simplify the expression
`(14x^(20)y^(10))/((2*14*x^(12) y^(14) )^(4))` first we need to raise every member of the denominator to the given exponent, number 4

Remember that
`(x^(b) )^(c) =z^(b*c)` where 'a' and 'b are natural numbers (any numbers you want

`(14x^(20)*y^(10))/(2^(4)*14^(4)*x^(48)*y^(56))`

Where we can make some operations, remember that
`(x^(a) )/(x^(c) )=x^(a-c)`

`(1)/(2^(4)*14^(3) *x^(28)*y^(46))`

We have assumed that nor x, nor y equals 0 in any moment, since if that would happen, we ca not simplify anything bacause error math 0/0.