Question

I need help simplifying #6

Answer 1

Therefore,

`(24x^(5)y^(9)z^(-8))/(10x^(-3)y^(4)z^(-4))=(12x^(8)y^(5))/(5z^(4))`

Explanation:

Simplify

`(24x^(5)y^(9)z^(-8))/(10x^(-3)y^(4)z^(-4))`

Solution:

Using the Identities

`1.\ x^(-a)=(1)/(x^(a))`

`2.\ (1)/(x^(-a))=x^(a)`

`3.\ (x^(a))/(x^(b))=x^((a-b))`

Therefore,

`(24x^(5)y^(9)z^(-8))/(10x^(-3)y^(4)z^(-4))=(24x^((5+3))y^((9-4))z^((-8+4)))/(10)`

`(24x^(5)y^(9)z^(-8))/(10x^(-3)y^(4)z^(-4))=(2* 12x^(8)y^(5)z^(-4))/(2* 5)`

`(24x^(5)y^(9)z^(-8))/(10x^(-3)y^(4)z^(-4))=(12x^(8)y^(5))/(5z^(4))`

Therefore,

`(24x^(5)y^(9)z^(-8))/(10x^(-3)y^(4)z^(-4))=(12x^(8)y^(5))/(5z^(4))`

Answer 2

The simplified expression is
`(12x^8y^5)/(5z^4)`

Therefore
`(24x^5y^9z^(-8))/(10x^(-3)y^4z^(-4))=(12x^8y^5)/(5z^4)`

Explanation:

Given expression is
`(24x^5y^9z^(-8))/(10x^(-3)y^4z^(-4))`

To simplify the given expression as below :

`(24x^5y^9z^(-8))/(10x^(-3)y^4z^(-4))`

`=(12x^5y^9z^(-8))/(5x^(-3)y^4z^(-4))`

`=(12x^5y^9z^(-8)x^3y^(-4)z^4)/(5)` ( by using the property
`a^(m)=(1)/(a^(-m))` )

`=(12x^5.x^3.y^9.y^(-4)z^(-8)z^4)/(5)`

`=(12)/(5)x^(5+3).y^(9-4).z^(-8+4)` ( by using the property
`a^m.a^n=a^(m+n)` )

`=(12)/(5)x^8y^5z^(-4)`

`=(12x^8y^5)/(5z^4)` ( by using the property
`a^(-m)=(1)/(a^m)` )

`(24x^5y^9z^(-8))/(10x^(-3)y^4z^(-4))=(12x^8y^5)/(5z^4)`

The simplified expression is
`(12x^8y^5)/(5z^4)`

Therefore
`(24x^5y^9z^(-8))/(10x^(-3)y^4z^(-4))=(12x^8y^5)/(5z^4)`