How do you solve the following problems:
What is the area of a square with the length of a side equaling 3a^5?
I got (3a^5)(3a^5)=9a^10 is that correct??
What is the area of the rectangle with the width of 6x^2 and the length of 12x^3?
I got 6*5^2=900; 12*5^3=216,000 for a total of 216,900 is that correct?
If they are wrong can you show me how to do them? THANKS
yes, (3a^5)^2 = 9a^10
6x^2 * 12x^3 = 72x^5
Why did you assume x=5?
oh sorry on the worksheet it said to evaluate each monomial for x=5, y=-1, and z=4
Steve: was my answer correct? 216,900?
To solve the first problem, you are trying to find the area of a square with a side length of 3a^5. The formula to calculate the area of a square is simply side length squared. So in this case, you would square the side length of 3a^5.
To square a term with an exponent, you multiply the exponent by itself. So (3a^5)^2 would be (3^2)(a^5)^2. Simplifying further, (3^2) is 9, and (a^5)^2 is a^10. Therefore, the area of the square is 9a^10. Your answer, 9a^10, is correct!
Now, moving on to the second problem, you are given the dimensions of a rectangle with a width of 6x^2 and a length of 12x^3. Again, the formula for finding the area of a rectangle is length multiplied by width.
To find the area, you multiply the length and the width together. So, (6x^2)(12x^3) would be (6 * 12)(x^2 * x^3). Simplifying further, 6 * 12 is 72, and x^2 * x^3 is x^(2+3) = x^5. Therefore, the area of the rectangle is 72x^5.
Based on your calculations, you got 900 for the width and 216,000 for the length, and added them together to get 216,900 as the total. However, this seems to be a calculation mistake.
The correct answer is 72x^5. It's important to pay attention to the operations and multiplication rules when simplifying expressions.