Question

Choose the correct simplification of x to the 3rd power over y to the 5th power all raised to the 2nd power.

x to the 5th power over y to the 7th power
x over y to the 3rd power
x to the 6th power over y to the 10th power
x6y10

Answer 1

`\left( \cfrac{x^3}{y^5} \right)^2=\cfrac{(x^3)^2}{(y^5)^2}=\cfrac{x^(3*2)}{y^(5*2)}=\cfrac{x^(6)}{y^(10)}`

Answer 2

Option 3 - x to the 6th power over y to the 10th power

Explanation:

Given : Expression x to the 3rd power over y to the 5th power all raised to the 2nd power.

To find : Choose the correct simplification of the expression?

Solution :

Writing the expression in value form,

x to the 3rd power =
`x^3`

y to the 5th power=
`y^5`

x to the 3rd power over y to the 5th power all raised to the 2nd power =

`((x^3)/(y^5))^2`

Now applying identity,

`((x)/(y))^a=(x^a)/(y^a)`

`=((x^3)/(y^5))^2`

`=((x^3)^2)/((y^5)^2)`

Using identity,
`(x^a)^b=x^(a.b)`

`=(x^(3.2))/(y^(5.2))`

`=(x^(6))/(y^(10))`

In word form, x to the 6th power over y to the 10th power.

Therefore, Option 3 is correct.