Final answer:
The expression (15n)⁴ denotes the product of 15 and a number n, raised to the fourth power, which means 15n is multiplied by itself four times, resulting in 15⁴ * n⁴. This shows how integer exponents are used to indicate repeated multiplication.
Step-by-step explanation:
The question is asking for the result of taking the product of 15 and another number, let's call it n, and then raising this product to the fourth power. This can be expressed mathematically as (15n)⁴. To understand this concept, let's use the example of 53 and raising it to the fourth power. It simplifies to 512, because you multiply the exponents (3 and 4) to get the result. This multiplication results in the original value of 5 being raised to the twelfth power, which is 5 multiplied by itself twelve times.
In general, when a number is raised to an integer power, we are simply multiplying the number by itself as many times as the exponent indicates. Therefore, the expression (15n)4 means you would multiply 15n by itself four times. The outcome would be (15n) x (15n) x (15n) x (15n), or 154n⁴. In this situation, the value of the expression becomes significantly larger and will be sixteen times the square of the original value of 15n, given that n⁴ results in n being multiplied four times.