Short Answer

Question

Note: Your teacher will grade your response to ensure you receive proper credit for your answer.
List three different ways to write 511 as the product of two powers. Explain why all three of your expressions are equal to 511.

Answer 1

1) 511 = 7 × 73
In this case, we have two prime numbers multiplied together, which directly gives the result 511.

2) 511 = 1 × 511
Since any number multiplied by 1 is that number itself, multiplying 1 by 511 results in 511.

3) 511 = 13 × 3^3
In this case, we have 13 multiplied by the cube of 3 (3^3 = 27). The product of 13 and 27 equals 511.

All three expressions are equal to 511 because they represent different ways to multiply two numbers, or powers, to obtain the same result. These expressions showcase that numbers can have various factors or combinations that give the same product, which in this case, is 511.