Question

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

N = 3 x 5² x x³
Express 5N² as a product of prime factors in index form.
Give your answer in terms of x.

Answer 1

To express 5N² as a product of its prime factors in index form, we square the prime factors of N and multiply by 5, resulting in 3² × 5¶ × x¶.

Step-by-step explanation:

The question requires expressing 5N² as a product of prime factors in index form. We know that N is 3 × 5² × x³. To find 5N², we start by multiplying N by 5, which gives us 5 × 3 × 5² × x³. We then need to square this entire expression to get 5N².

When squaring, we use the power rule which tells us that (a·b)² = a²·b². Therefore, the squared expression is 5² × 3² × 5´ × x¶. Combining the powers of 5, this simplifies to 3² × 5¶ × x¶, which is the final expression for 5N² in terms of prime factors with their exponents.