Answer:
Expression will be 5[tex]N^{2}[/tex] = [tex]3^{2}[/tex]×[tex]5^{5}[/tex]×[tex]x^{6}[/tex]
Step-by-step explanation:
As given in the question a number N is expressed as a product of its prime factors in index form is N = 3×[tex]5^{2}[/tex]×[tex]x^{3}[/tex]
Now we have to express 5[tex]N^{2}[/tex] as a product of prime factors in index form.
For this we write the equation N×N= (3×[tex]5^{2}[/tex]×[tex]x^{3}[/tex])×((3×[tex]5^{2}[/tex]×[tex]x^{3}[/tex])
[tex]N^{2}[/tex]=3×3×[tex]5^{2}[/tex]×[tex]5^{2}[/tex]×[tex]x^{3}[/tex]×[tex]x^{3}[/tex]
[tex]xN{2}[/tex] = [tex]3^{2}[/tex]×[tex]5^{4}[/tex]×[tex]x^{6}[/tex]
Then 5[tex]N^{2}[/tex] = 5×[tex]3^{2}[/tex]×[tex]5^{4}[/tex]×[tex]x^{6}[/tex]
5[tex]N^{2}[/tex] = [tex]3^{2}[/tex]×[tex]5^{5}[/tex]×[tex]x^{6}[/tex]
