Question

Given that the cube root of 27 is 3, what is 27^4/3?

Answer 1

What is the correct simplification of 25^3/2?

Answer 2

To solve this problem, we can use a basic property of exponents: (a^m)^n = a^(m*n).

Using this property, we can rewrite 27^(4/3) as (3^3)^(4/3).

Since (a^m)^n = a^(m*n), we can simplify (3^3)^(4/3) to 3^(3*(4/3)) = 3^(4).

Therefore, 27^(4/3) = 3^4 = 81.

Answer 3

To simplify 25^(3/2), we need to first recognize that raising a number to the power of 1/2 is equivalent to taking the square root of that number.

Thus, 25^(3/2) can be written as (25^(1/2))^3.

The square root of 25 is 5, so we have (5)^3.

Calculating (5)^3, we get 5^3 = 5 × 5 × 5 = 125.

Therefore, the correct simplification of 25^(3/2) is 125.