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

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

$={(2*3*3^{2})^{\frac{1}{2}}*(x^{8}*x)^{\frac{1}{2}}*(y^{6}*y)}^{\frac{1}{2}}$

$={(2*3)^{\frac{1}{2}}*(3^{2})^{\frac{1}{2}}*(x^{8})^{\frac{1}{2}}*(x)^{\frac{1}{2}}*(y^{6})^{\frac{1}{2}}*(y)}^{\frac{1}{2}}$

$={(2*3*x*y)^{\frac{1}{2}}*(3)*(x^{4})*(y^{3})$

$=3x^{4}y^{3}\sqrt{6xy}$

therefore

the answer is

$3x^{4}y^{3}\sqrt{6xy}$

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.