Question

I'm having trouble with this question can someone help me, please!!!

Answer 1

Answer:
[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
The last option is the correct one

Explanation:
Te given is:
[7^(1/3)]^3 which means that we will multiply 7^(1/3) by itself three times
So, the first step is:
[7^(1/3)]^3 = 7^(1/3) * 7^(1/3) * 7^(1/3)
Now, when multiplying numbers with same base, the powers are added together.
Here, we have the same base (7), so we will add the powers.
So, the next step is:
7^(1/3) * 7^(1/3) * 7^(1/3) = 7^(1/3 + 1/3 + 1/3)
Now, 1/3 + 1/3 + 1/3 = 3/3 which is equal to 1
So, the third step is:
7^(1/3 + 1/3 + 1/3)=7^(3/3) =7^1
Finally, any base raised to the power of one would be equal to itself.
So, the final step is:
7^(3/3) =7^1=7

Concatenating all the previous steps, we will find that the complete scenario is:
[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

Hope this helps :)

Answer 2

Answer: It is the last option:

$(7^{ \frac{1}{3} })^{3} =7^{ \frac{1}{3}}.7^{ \frac{1}{3}}.7^{ \frac{1}{3} }=7^{ \frac{1}{3} + \frac{1}{3} + \frac{1}{3} } =7^{ \frac{3}{3}}=7^1=7$

Justification:

step      explanation

1)           By definition (A)^3 = A*A*A, so replace A with $7^{ \frac{1}{3} }$

2)           use the property of multiplication of powers with the same base

3)           add the fractions

4)           simplify 3/3 = 1

5)           a base raised to power 1 is the same base.