Question

What is the answer ......................

Answer 1

$5N^2=2^2 \times 5^{7} \times x^{8}$

Solution:

Given a number N in product of its prime factors.

$N=2 \times 5^{3} \times x^{4}$

Now, express $5 N^{2}$ as a product of prime factors in index form.

Substitute $2 \times 5^{3} \times x^{4}$ in place of N.

$5N^2=5\times(2 \times 5^{3} \times x^{4})^2$

Use exponential rule: $\left(a^{m}\right)^{n}=a^{m n}$

Multiply the power 2 into the powers of factors of every number in the bracket.

$5N^2=5\times2^2 \times 5^{6} \times x^{8}$

Arrange like terms together.

$5N^2=2^2 \times 5\times 5^{6} \times x^{8}$

Use exponential rule: $a^{m} \times a^{n}=a^{m+n}$

$5N^2=2^2 \times 5^{1+6} \times x^{8}$

$5N^2=2^2 \times 5^{7} \times x^{8}$

Hence $5N^2=2^2 \times 5^{7} \times x^{8}$.