Question

What is the simplest radical form of 8 to the two thirds power?

(a) 4
(b) 2√2
(c) 2√3
(d) 8√2

Answer 1

The simplest radical form of 8 to the two-thirds power is 4, after taking the cube root of 8, which is 2, and then squaring that result. The correct answer is (a) 4.

Step-by-step explanation:

To find the simplest radical form of 8 raised to the two-thirds power, we can use the property of exponents that states that taking the square root of a number is equivalent to raising the number to the one-half power. Since the exponent of 2/3 in this case is not one-half, we can't directly apply this property. Instead, we can rewrite the exponent as a fractional power: 8^(2/3) = (8^2)^(1/3) = 64^(1/3).

The cube root of 64 is 4, so the simplest radical form of 8^(2/3) is 4.

The simplest radical form of 8 to the two-thirds power involves understanding exponents and radicals. According to the exponent rules, a fractional exponent ⅓ indicates a cube root and ² indicates squaring. To simplify 8 to the two-thirds power, we can rewrite it as the cube root of 8 squared.

First, we calculate the cube root of 8:

• ∛8 = 2

Now, we square the result:

• 2² = 4

Thus, the simplest radical form of 8 to the two-thirds power is 4, which corresponds to option (a).