Question

Which expression is equivalent to (4x^3y^5) (3x^5y)^2 ?

Answer 1

(3x^5y)^2=
3^2=9
(x^5)^2=x^10
y^2=y^2

(3x^5y)^2=9x^10y^2

9x^10y^2(4x^3y^5)=
9*4=36
x^10*x^3=x^13
y^2*y^5=y^7
9x^19y^2(4x^3y^5)= 36x^13y^7

Final answer: B

Answer 2

Answer:  Option 'B' is correct.

Step-by-step explanation:

Since we have given that

$(4x^3y^5).(3x^5y)^2$

We will use "law of exponents" i.e.

$(ab)^m=a^m\times b^m$

so our expression becomes,

$(4x^3y^5).(3x^5y)^2\\\\=4x^3y^5\times 3^2(x^5)^2y^2\\\\=4x^3y^5\times 9x^{10}y^2\\\\=36x^3y^5\times x^{10}y^2$

Now. again we will use " Law of exponents" i.e.

$a^m\times b^m$

so, our expression becomes,

$36x^3y^5\times x^{10}y^2\\\\=36x^{3+10}y^{5+2}\\\\=36x^{13}y^{7}$

Hence, Option 'B' is correct.