Understanding Exponentiation
Exponentiation is a mathematical operation involving two numbers, the base and the exponent. In this case, you are asking about 8 to the power of 2 to the power of 3, which can also be expressed as 8^(2^3). To break this down, we need to follow the order of operations.
Step 1: Calculate the Exponent
First, we need to evaluate the exponent 2 to the power of 3.
- 2^3 = 2 × 2 × 2 = 8
This calculation shows us that 2 raised to the power of 3 equals 8.
Step 2: Use the Result as the Exponent for 8
Now that we know that 2^3 = 8, we can replace that in our original problem:
- 8^(2^3) = 8^8
Step 3: Calculate 8 to the Power of 8
Now, it’s time to calculate 8 to the power of 8. This can be done either through repeated multiplication or using a calculator to find the exact value.
- 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8
Each multiplication gives us:
- 8^1 = 8
- 8^2 = 64
- 8^3 = 512
- 8^4 = 4096
- 8^5 = 32768
- 8^6 = 262144
- 8^7 = 2097152
- 8^8 = 16777216
Therefore, the final result of 8 to the power of 2 to the power of 3 is:
Conclusion:
8^(2^3) = 8^8 = 16777216