I'll give it a shot. 1. The expression (y to the 7th plus z to the 4th) raised to the zero power is equal to 1. That's because any quantity to the zero power is equal to one. So for this situation you may simply ignore that expression. Now, y to the -3 is in the numerator. Move it to the denominator (bottom of the fraction) and change it to y to the 3rd (drop the minus sign). In the same manner, move the x to the -4 from the bottom to the top of the fraction (the numerator) and change it to x to the 4th (drop the minus sign). Divide both the 9 and the 12 by 3. In other words, reduce the 9/12 to 3/4. Now the numerator is 3 x to the 8th z to the 8th. The denominator is 4 y to the 3rd. AND, all of that is inside of brackets and raised to the -3rd. Turn the fraction upside down (that is, write its reciprocal) and drop the minus sign of the 3rd power. Finally, raise each factor in the top and bottom of the fraction to the 3rd power. The answer is 64 y to the 3rd over 27 x to the 8th z to the 8th. I wish I was showing you face-to-face and on a chalkboard -- it sure would be easier!
2. On this one, start from the inside and work out. The biggest "trick" is remembering to distribute the minus signs throughout the various parentheses and brackets. Here we go: 2ab-{7ab-[2a-2ab-8(2b-ab)]}+ab becomes, 2ab-{7ab-[2a-2ab-16b+8ab]}+ab then, 2ab-{7ab-2a+2ab+16b-8ab}+ab and, 2ab-7ab+2a-2ab-16b+8ab+ab combine the like terms, 2ab-7ab-2ab+8ab+ab+2a-16b (I just rearranged them) finally: 2ab+2a-16b is the answer. You were real close on that one! Looks like you missed a sign-change somewhere.
3. This one is much easier to explain. The area of a triangle is 1/2 times the base times the height. (A= 1/2 bxh) So your triangle area is 1/2 of 2x4, or 1x4, or even 2x2=4 square inches. You see, it doesn't matter whether you use half of the base and multiply by the height, or use half of the height and multiply by the base, or just multiply the base by the height and then take half of the product! It's a beautiful thing.
I sure hope this is helpful to you. Best of luck. Tom
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Today's Featured Article - Old Time Threshing - by Anthony West. A lovely harvest evening late September 1947, I was a school boy, like all school boys I loved harvest time. The golden corn ripens well and early, the stoking, stacking,.... the drawing in with the tractors and trailers and a few buck rakes thrown in, and possibly a heavy horse. It would be a great day for the collies and the terrier dogs, rats and mice would be at the bottom of the stacks so the dogs, would have a busy time hunting and killing, all the corn was gathered and ricked in what we c
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