Question

Simplify 54x9 y7 .
A) 3x4 y3 6 B) 3x4 y3 6xy C) 9x4 y3 6xy D) 9x3 y3 6xy

Answer 1

we have

`\sqrt{54x^(9)y^(7)}`

we know that

`54=2*3^(3) =2*3*3^(2)\\ x^(9)= x^(8)*x \\ y^(7)=y^(6)*y`

Substitute

`\sqrt{(2*3*3^(2))*(x^(8)*x)*(y^(6)*y)}=[{(2*3*3^(2))*(x^(8)*x)*(y^(6)*y)}]^{(1)/(2)} \\ \\`

`={(2*3*3^(2))^{(1)/(2)}*(x^(8)*x)^{(1)/(2)}*(y^(6)*y)}^{(1)/(2)}`

`={(2*3)^{(1)/(2)}*(3^(2))^{(1)/(2)}*(x^(8))^{(1)/(2)}*(x)^{(1)/(2)}*(y^(6))^{(1)/(2)}*(y)}^{(1)/(2)}`

`={(2*3*x*y)^{(1)/(2)}*(3)*(x^(4))*(y^(3))`

`=3x^(4)y^(3)√(6xy)`

therefore

the answer is

`3x^(4)y^(3)√(6xy)`

Answer 2

Simplify the square root of 54x^9y^7 or √(54x^9y^7)

54x^9y^7 = (3x^4y^3)^2 (6xy)

Now square root of (3x^4y^3)^2 = 3x^4y^3

So the final answer is 3x^4y^3 √(6xy)

Hence option “B” is correct.