Question

Select the simplification that accurately explains the following statement.

∛7 = 7^(1/3)

A. (7^(1/3))^3 = 7^(1/3) · 7^(1/3) · 7^(1/3) = 7^(1/3 + 1/3 + 1/3) = 7^(3/3) = 7^1 = 7

B. (7^(1/3))^3 = 7^(1/3) · 7^(1/3) · 7^(1/3) = 7 · 7^(1/3) = 3 · (1/3) · 7 = 1 · 7 = 7

C. (7^(1/3))^3 = 7^(1/3) · 7^(1/3) · 7^(1/3) = 7 · (1/3 + 1/3 + 1/3) = 7 · (3/3) = 7 · 1 = 7

D. (7^(1/3))^3 = 7^(1/3) · 7^(1/3) · 7^(1/3) = 7^(1/3) · (1/3) · (1/3) = 7^(3/3) = 7^1 = 7

Answer 1

The correct simplification is option A, which correctly applies the laws of exponents to show that cubing the cube root of 7 yields the original number 7.

Step-by-step explanation:

The correct simplification for the expression ∛7 = 7^(1/3) is shown in option A. This can be understood by following the laws of exponents, where when we multiply exponents with the same base, we add the exponents together. The calculation goes as follows:

• (7^(1/3))^3 = 7^(1/3) · 7^(1/3) · 7^(1/3) = 7^(1/3 + 1/3 + 1/3) = 7^(3/3) = 7^1 = 7

This simplification illustrates that raising a number to the 1/3 power and then cubing the result (raising it to the power of 3) results in the original number, confirming the basic properties of roots and powers.