Question

How (-8)⁴/³) can be evaluated using properties of rational exponents to result in an integer answer.

Answer 1

To evaluate (-8)4/3, we compute the cube root of -8 to get -2, then raise -2 to the 4th power to get 16, which is an integer.

Step-by-step explanation:

The student is asking how to evaluate the expression (-8)4/3 using properties of rational exponents to find an integer answer. Rational exponents can be interpreted in terms of roots and powers. The exponent 4/3 means that we should raise (-8) to the 4th power and then take the cube root, or equivalently, take the cube root of (-8) first and then raise it to the 4th power.

The cube root of -8 is -2 because (-2)3 = -8. Taking that result and raising it to the 4th power gives us (-2)4 = 16, which is the integer answer we're seeking.

In a step-by-step explanation:

1. Start with (-8)4/3.
2. Take the cube root of -8, which is -2.
3. Raise -2 to the 4th power: (-2)4 = 16.