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

Asked by maham237 @ 15/12/2020 in Mathematics viewed by 357 People

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

Answered by maham237 @ 15/12/2020

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 $8^{\frac{1}{3}}$ . 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

$8^{\frac{1}{3}}=(2^3)^{\frac{1}{3}}=2^{3\times \frac{1}{3}}=2^{\frac{3}{3}}=2^1=2$

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

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