Question

(−5)3x7(yz)4 / (3)2x2y8z2

Answer 1

`((-5)3x^7(yz)^4)/((3)2x^2y^8z^2)=(-5x^5z^2)/(2y^4)`

Explanation:

Given:

The expression to simplify is given as:

`((-5)3x^7(yz)^4)/((3)2x^2y^8z^2)`

In order to simplify this, we have to use the law of indices.

1.
`(ab)^m=a^mb^m`

So,
`(yz)^4=y^4z^4`

Substitute this value in the above expression. This gives,

`=((-5)3x^7y^4z^4)/((3)2x^2y^8z^2)\\\\\\=(-15x^7y^4z^4)/(6x^2y^8z^2)......(-5* 3=15\ and\ 3* 2=6)`

Now, we use another law of indices.

2.
`(a^m)/(a^n)=a^(m-n)`

So,
`(x^7)/(x^2)=x^(7-2)=x^5,(y^4)/(y^8)=y^(4-8)=y^(-4), (z^4)/(z^2)=z^(4-2)=z^2`

Substitute these values in the above expression. This gives,

`=(-15)/(6)* x^5* y^(-4)* z^2\\\\=(-5x^5y^(-4)z^2)/(2)`

Finally, we further simplify it using the law
`a^(-m)=(1)/(a^m)`

So,
`y^(-4)=(1)/(y^4)`

Therefore, the given expression is simplified as:

`((-5)3x^7(yz)^4)/((3)2x^2y^8z^2)=(-5x^5z^2)/(2y^4)`