Question

Expressed as a product of its prime factors in index form, a number N is

N=3 X 5^2 X x^3

Express 5N^2 as a product of prime factors in index form.
Give your answer in terms of x.

Answer 1

`5N^2=3^(2) * 5^(5) * x^(6)`

Step-by-step explanation

`N=3*5^2 * x^3`.

`5N^2=5(3*5^2 * x^3)^2`

Recall this property of exponents;

`(a^m)^2=a^(m) * a^m`

So our product becomes;

`5N^2=5(3*5^2 * x^3) * (3*5^2 * x^3)`

`5N^2=5* 3* 3 * 5^2 * 5^2 * x^3 * x^3`

`5N^2=3* 3* 5 * 5^2 * 5^2 * x^3 * x^3`

Recall this law of exponents:

`a^m * a^n =a ^(m+n)`

`5N^2=3^(1+1) * 5^(1+2+2) * x^(3+3)`

`5N^2=3^(2) * 5^(5) * x^(6)`