How much is 81 to the power of 3/4?

In algebra, the method of expressing powers and roots together is known as a fractional exponent.

Answer: 81 to the power of 3/4 is 27.

Let's see the solution step by step.

Explanation:

Given: 81 to the power of 3/4 or 81^(3/4).

First, rewrite 81 as 3⁴.

81^(3/4) = 3^4(3/4)

Apply one of the rules of exponents, (a^m)ⁿ = a^mn.

So we cancel the common factor of 4 to get,

3³ = 3 × 3 × 3 = 27

Thus, 81 to the power of 3/4 is 27.