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Here is a task from my son's math paper:

enter image description here

The problem is besides not knowing how to simplify this expression (my math was terribly bad at school and it's already been a long time since that time) I can't quite get it whether it is 125 raised to the power of two or the whole cubic root raised to the power of two.

Can anyone, please, for whom such tasks are a breeze help me determine the exact expression in this task and also give me a clue on how to simplify that expression?

Thank you in advance. Just in case: my son is in the 10th grade, that is, the first grade of senior high school.

brilliant
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    Please ask your son to post the question. Then, your son can be asked to show the work that he has done. – user2661923 Apr 10 '22 at 11:21
  • @user2661923 - We were posting this question together. He himself doesn't know whether it's 125 raised to the power of 2 or the whole root raised to the power of 2. It's not clear on the paper. So, he hasn't done any work because he doesn't understand the task in the first place. – brilliant Apr 10 '22 at 11:28
  • The powers of 6 on the 2 and of 2 on the 3 under the radical are clearly only on the number 2 and 3 under the radical. If the power of 3 was only on the 125 it would have been written that way like the other two power under the radical. But the power of 3 appears after th radical so is done then. – coffeemath Apr 10 '22 at 11:34
  • @coffeemath - I don't understand what you are saying. Where is the power of 3 in that task? – brilliant Apr 10 '22 at 11:37
  • @brilliant When I see $3^2$ I say that 2 is the power on the 3. [the power is 2, the base is 3.] At the end I should have been talking of the power of 2 on the 125 rather than the power of 3 on the 125. {sorry] – coffeemath Apr 10 '22 at 12:35

1 Answers1

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The expression is $$\left(\sqrt[3]{-(2^6) \times (3^2) \times 125}\right)^2$$ $$ = (-1 \times 2^6 \times 3^2 \times 5^3)^{2/3}$$ $$ = ((-1)^{1/3})^2 \times 2^4 \times 3^{4/3} \times 5^2$$ $$ = (-1)^2 \times 2^4 \times 3 \times 3^{1/3} \times 5^2$$ $$= 1 \times 2^4 \times 3 \times 5^2 \times \sqrt[3]{3}$$ $$ = 1200\sqrt[3]{3}$$