Question

Expressed as a product of its prime factors in index form a number N is
N=3 times 5 to the power of 2 times x to the power of 3.

Express 5n to the power of 2 as a product of its prime factors in the index form. Give your answer in terms of x.

Answer 1

Answer:

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.

Answer 2

Answer:

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^3N=3x×5

2

x×x

3

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

2

x×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

2

x)

2

×(3x)

2

×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.