Question

Put these numbers in order from smallest to largest:

A) \(1^8\)
B) \(2^4\)
C) \(3^3\)
D) \(5^2\)

Answer 1

To arrange the given numbers in ascending order, we need to evaluate each of them and then compare their values. The correct order is option A,B,D and C. .

Explanation :

Let's go through each of the numbers:

A) \(1⁸\):
Raising any non-zero number to any power will give us the number itself. Since we have 1 here, and anything raised to any power is still 1, \(1^8\) is equal to 1.

B) \(2⁴\):
When we multiply 2 by itself four times, we get \(2 \times 2 \times 2 \times 2\) which equals 16.

C) \(3^3\):
When we multiply 3 by itself three times, we get \(3 \times 3 \times 3\) which equals 27.

D) \(5²\):
When we multiply 5 by itself two times, we get \(5 \times 5\) which equals 25.

Now that we have the value of each number:
- A is 1
- B is 16
- C is 27
- D is 25

We can compare them to determine the order from smallest to largest:
1 (smallest), 16, 25, 27 (largest).

Thus, the correct order is: A) \(1₈\), B) \(2⁴\), D) \(5²\), C) \(3³\).

Answer 2

The numbers in order from smallest to largest are:

A) 1^8,

D) 5^2,

C) 3^3,

B) 2^4.

Step-by-step explanation:

Starting with the given numbers:

A) 1^8 = 1

B) 2^4 = 16

C) 3^3 = 27

D) 5^2 = 25

Comparing these values, the smallest number is A) 1^8 = 1 because any number raised to the power of 1 remains itself. The next smallest is D) 5^2 = 25 followed by C) 3^3 = 27, and the largest number is B) 2^4 = 16.

While 2^4 might seem larger than 3^3 at first glance, the exponential growth rate changes this comparison. 3^3 or 27 exceeds 2^4 or 16 because 3 raised to the power of 3 results in a higher value due to the higher base number despite the smaller exponent. The sequence from smallest to largest is 1, 25, 27, and 16.

This ordering aligns with the exponential growth rates of the numbers. Despite the exponents involved, the base numbers play a crucial role in determining the overall size of the value, as seen in 3^3 surpassing 2^4 due to the base number 3 being greater than 2. Hence, the order is based on both exponentiation and the magnitude of the base numbers.