MHB Applying the laws of exponents

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The discussion focuses on verifying answers related to simplifying expressions using the laws of exponents. For the first problem, the participant simplifies (5x^3yz^2)^2(-3x^3y^4z) and arrives at -75x^9y^6z^5, which is confirmed as correct. In the second problem, they simplify 8a^-2b^3c^4/18a^5b^-3c to get 4b^6c^3/9a^7, which is also validated as correct. The participant expresses a need for assistance due to a lack of real-life support for these math problems. Overall, both answers provided are confirmed to be accurate.
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Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :)

PART A

7) Simplify (5x^3yz^2)^2(-3x^3y^4z)

My answer: -75x^9y^6z^5

8) Simplify the problem below using positive exponents only.

8a^-2b^3c^4
18a^5b^-3c

My Answer:
4b^6c^3
9a^7
 
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Re: Please check my answers - 4

drop said:
Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :)

PART A

7) Simplify (5x^3yz^2)^2(-3x^3y^4z)

My answer: -75x^9y^6z^5

8) Simplify the problem below using positive exponents only.

8a^-2b^3c^4
18a^5b^-3c

My Answer:
4b^6c^3
9a^7

Both correct.

I underlined your numerators there. :)
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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