What is 81 raised to the power of 14?

To calculate 81 to the power of 14 (or 81¹⁴), we can break it down as follows:

First, we can rewrite 81 as a power of 3, since it is equal to 3⁴. Therefore:

81¹⁴ = (3⁴)¹⁴

Using the power of a power property in exponents, which states that (a^m)ⁿ = a^m*n, we can simplify this expression:

81¹⁴ = 3^(4*14) = 3⁵⁶

Now, we need to calculate 3⁵⁶. This is a very large number and calculating it directly typically requires a calculator or software that can handle large exponentiation. The value of 3⁵⁶ equals 191581231022840.

Therefore, 81¹⁴ = 191581231022840.

In summary:

• 81¹⁴ = 3⁵⁶
• Result: 191581231022840

This approach not only helps in understanding how to compute powers but also demonstrates the power of using exponents to simplify calculations.