Question

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

Answer 1

ANSWER

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

EXPLANATION

$N=3\times5^2 \times x^3$.

$5N^2=5(3\times5^2 \times x^3)^2$

Recall this property of exponents;

$(a^m)^2=a^{m} \times a^m$

So our product becomes;

$5N^2=5(3\times5^2 \times x^3) \times (3\times5^2 \times x^3)$

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

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

Recall this law of exponents:

$a^m \times a^n =a ^{m+n}$

$5N^2=3^{1+1} \times 5^{1+2+2} \times x^{3+3}$

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