Calculating 81 to the power of 34 results in a very large number. To express it, we can first break down the problem. The base, 81, can be rewritten as 3^4 because 81 = 3 × 3 × 3 × 3. Therefore, 81^34 can be expressed as:
(3^4)^34
Using the power of a power rule in exponents, we multiply the exponents:
3^(4 × 34) = 3^136
This means that 81 to the power of 34 is equivalent to 3 raised to the power of 136. The actual number is extremely large and has many digits. It’s often more practical to work with such numbers in exponential form rather than calculating their full decimal representation. Thus, we say:
8134 = 3136