Question

Choose the correct simplification of x to the 12th power times z to the 11th power all over x to the 2nd power times z to the 4th power. x10z7 x14z15 1 over x to the 10th power times z to the 7th power 1 over x to the 14th power times z to the 15th power

Answer 1

A) is correct answer.

Explanation:

I took the FLVS Algebra 1 lesson 6.08 quiz

Answer 2

The option A)
`x^(10)z^7` is correct answer.

The correct simplification for the given expression
`(x^(12)* z^(11))/(x^2* z^4)` is
`x^(10)z^7`

Explanation:

Given expression is x to the 12th power times z to the 11th power all over x to the 2nd power times z to the 4th power.

The given expression can be written as
`(x^(12)* z^(11))/(x^2* z^4)`

To choose the correct simplification of the given expression :

Now we have to simplify the given expression as below

`(x^(12)* z^(11))/(x^2* z^4)`

`=x^(12)* z^(11)(x^(-2)* z^(-4))` ( by using the identity
`(1)/(a^m)=a^(-m)` )

`=(x^(12).x^(-2))* (z^(11).z^(-4))`

`=x^(12-2)* z^(11-4)` ( by using the identity
`a^m.a^n=a^(m+n)` )

`=x^(10)* z^7`

`=x^(10)z^7`

∴
`(x^(12)* z^(11))/(x^2* z^4)=x^(10)z^7`

The correct simplification for the given expression
`(x^(12)* z^(11))/(x^2* z^4)` is
`x^(10)z^7`

Hence option A)
`x^(10)z^7` is correct answer.