Question

Which of the following shows the correct steps to find the value of 8 to the power of 1 over 3?

1) 8 to the power of 1 over 3 equals 2 to the power of 3 to the power of 1 over 3 equals 2 to the power of 3 multiplied by 1 over 3 equals 2
2) 16 to the power of 1 over 4 equals 8 to the power of 2 to the power of 1 over 4 equals 8 to the power of 2 multiplied by 1 over 4 equals 8
3) 8 to the power of 1 over 3 equals 2 to the power of 4 to the power of 1 over 3 equals 2 to the power of 4 multiplied by 1 over 3 equals 16
4) 8 to the power of 1 over 3 equals 4 to the power of 3 to the power of 1 over 3 equals 4 to the power of 3 multiplied by 1 over 3 equals 4

Answer 1

To calculate 8 to the power of 1/3, we apply the rules of exponents, realizing that (2^3)^(1/3) simplifies to 2^(3*1/3), which equals 2.

Step-by-step explanation:

To find the value of 8 to the power of 1 over 3 (81/3), we must first recognize that 8 is 23. Therefore, 81/3 is the same as (23)1/3. Now, we use the rule of multiplying exponentiated quantities, which tells us to multiply the exponents together. In this case, we're multiplying 3 by 1/3, which results in 1. So, (23)1/3 simplifies to 23*1/3 which is 21 or just 2.

To find the value of 8 to the power of 1 over 3, we need to rewrite it as a radical. The exponent 1/3 is equivalent to taking the cube root. So, 8 to the power of 1/3 is the same as the cube root of 8. Since the cube root of 8 is 2, the correct answer is 2.