Question

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

A) 24x^13y^7
B) 36x^13y^7
C) 36x^28y^6
D) 144x^16y^12

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.

Explanation:

Since we have given that

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

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

`(ab)^m=a^m* b^m`

so our expression becomes,

`(4x^3y^5).(3x^5y)^2\\\\=4x^3y^5* 3^2(x^5)^2y^2\\\\=4x^3y^5* 9x^(10)y^2\\\\=36x^3y^5* x^(10)y^2`

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

`a^m* b^m`

so, our expression becomes,

`36x^3y^5* x^(10)y^2\\\\=36x^(3+10)y^(5+2)\\\\=36x^(13)y^(7)`

Hence, Option 'B' is correct.