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.
Please help will mark as brainliest if right!

Answer 1

Given: N is a number which is expressed as a product of it's prime factors in index form.

$N=3 x\times 5^{2} x\times x^3$

Now, 5 N²= 5×$[3 x\times 5^{2} x\times x^3]^{2}$

               = $5 \times 9 x^{2} \times 5^{4}x^{2} \times} x^{6}$

                = $5\times(5^{2}x)^{2} \times(3x)^{2} \times x^{6}$

 = $5^{5}\times 3^{2}\times x^{10} {\text{using exponential properties } a^{m}\times a^{n}=a^{m+n} and [a^{m}]^{n}=a^{mn}$

 where 5 ,3,and x are different prime factors of 5N².

Answer 2

Answer:

= 3^2 * 5^5 * x^6

Step-by-step explanation:

Replace N in 5N^2 with

N=3*5^2*x^3

= 5(3 * 5^2 * x^3)^2 Using Law of

indices multiply the powers in the bracket

= 5 * 3^2 * 5^4 * x^6

= 3^2 * 5^5 * x^6