Middle School

Simplify [tex]54x^9 y^7[/tex].

A. [tex]3x^4 y^3 6[/tex]
B. [tex]3x^4 y^3 6xy[/tex]
C. [tex]9x^4 y^3 6xy[/tex]
D. [tex]9x^3 y^3 6xy[/tex]

Answer :

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.

we have

[tex]\sqrt{54x^{9}y^{7}}[/tex]

we know that

[tex]54=2*3^{3} =2*3*3^{2}\\ x^{9}= x^{8}*x \\ y^{7}=y^{6}*y[/tex]

Substitute

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

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

[tex]={(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}}[/tex]

[tex]={(2*3*x*y)^{\frac{1}{2}}*(3)*(x^{4})*(y^{3})[/tex]

[tex]=3x^{4}y^{3}\sqrt{6xy}[/tex]

therefore

the answer is

[tex]3x^{4}y^{3}\sqrt{6xy}[/tex]