Question

What expression is equivalent to 25 X 9y3

Answer 1

Answer: Last option.

Explanation:

You need to remember the Quotient of powers property:

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

Applying this property, we know that:

`\sqrt{(25x^9y^3)/(64x^6y^(11)) }=\sqrt{(25x^3)/(64y^8)}`

Descompose 25 and 64 into their prime factors:

`25=5*5=5^2\\64=8*8=8^2`

Since:

`\sqrt[n]{a^n}=a`

And according to the Product of powers property:

`(a^m)(a^n)=a^((m+n))`

You can simplify. So, the equivalent expression is:

`\sqrt{(5^2x^2*x)/(8^2y^8)}=(5x√(x) )/(8y^4)`

Answer 2

D

Explanation:

Use exponents property:

`(x^a)/(x^b)=x^(a-b)`

1. Note that

`(x^9)/(x^6)=x^(9-6)=x^3`

and

`(y^3)/(y^(11))=y^(3-11)=y^(-8)=(1)/(y^8)`

2. Now

`√(25)=5\\ \\√(64)=8\\ \\√(x^3)=x√(x)\\ \\\sqrt{(1)/(y^8)}=(1)/(y^4)`

So

`\sqrt{(25x^9y^3)/(64x^6y^(11))}=(√(25)√(x^3))/(√(64)√(y^8))=(5x√(x))/(8y^4)`

because
`x>0,\ y>0`