Question

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

8 to the power of 1 over 3 equals 4 to the power of 3 whole to the power of 1 over 3 equals 4 to the power of 3 multiplied by 1 over 3 equals 4

8 to the power of 1 over 3 equals 2 to the power of 3 whole to the power of 1 over 3 equals 2 to the power of 3 multiplied by 1 over 3 equals 2

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

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

Answer 1

The correct answer is: B

Step-by-step explanation:

Answer 2

The correct answer is:

8 to the power of 1 over 3 equals 2 to the power of 3 whole to the power of 1 over 3 equals 2 to the power of 3 multiplied by 1 over 3 equals 2

Explanation:

We are asked to evaluate
`8^{(1)/(3)}`. We know that if we raise a power to a power, we simplify it by multiplying the exponents; this will create a whole number exponent if we can rewrite 8 as a number to the 3rd power.

8 = 2(2)(2) = 2³

This means

`8^{(1)/(3)}=(2^3)^{(1)/(3)}=2^{3* (1)/(3)}=2^{(3)/(3)}=2^1=2`