Question

Simplify. Select "Not a real number" (-27)¹/³=3

Answer 1

The expression (-27)¹/³ simplifies to -1.

Step-by-step explanation:

The expression (-27)¹/³ can be simplified as follows:

1. First, we can rewrite -27 as (-3)³ because the cube of -3 is -27.
2. Next, we can apply the exponent rule for fractional exponents, which states that taking a negative number to a fractional exponent results in the reciprocal of the positive number raised to the same exponent.
3. So, (-27)¹/³ is equivalent to (1/(-3))¹/³. Using the rule for fractional exponents, we can rewrite this as 1¹/³ / (-3)¹/³.
4. Since any number raised to the 1/³ power gives the cube root of that number, we have 1/∛1 / ∛(-3).
5. The cube root of 1 is 1, so we have 1 / ∛(-3).
6. Finally, the cube root of -3 is -1, so the simplified expression is 1 / -1, which is equal to -1.