answer:1. Since any number raised to any power and then raised to the power of zero is 1, we have 3^{456} = 3^{0} = 1 because any nonzero number to the power of zero is 1. 2. For the division of powers, use the rule frac{a^m}{a^n} = a^{m-n}: [ 9^5 div 9^3 = 9^{5-3} = 9^2 ] Since 9 = 3^2, we have: [ 9^2 = (3^2)^2 = 3^4 = 81 ] 3. Add the results from steps 1 and 2: [ 1 + 81 = boxed{82} ]

answer:The brain of the computer is the CPU, and it does most of the thinking. RAM stores info for a short time, and the hard drive stores things for a long time.

answer:Let's break down the information given. We know the total cost of the bat and the ball together is 1.10. We also know the bat costs 1.00 more than the ball. To find the cost of the ball, let's denote the cost of the ball as x. Since the bat costs 1.00 more than the ball, the cost of the bat can be represented as x + 1.00. We can now create an equation that adds the cost of the bat and the ball, setting it equal to their total cost: x + (x + 1.00) = 1.10. Simplifying the equation, we get 2x + 1.00 = 1.10. Subtracting 1.00 from both sides gives 2x = 0.10. Dividing both sides by 2 results in x = 0.05. Therefore, the ball costs 0.05, or 5 cents.

answer:For the combined film reel to be divided into three equal parts that are integral, the total length of the film must be divisible by 3. First, let's find the total length of the film by adding the lengths of the two segments: 480 feet + 720 feet = 1200 feet. To determine if 1200 is divisible by 3, we can divide 1200 by 3 and check if the result is an integer. 1200 ÷ 3 = 400. Since 400 is indeed an integer, the total length of the film can be divided into three equal parts that are integral. This means the artist can divide the combined film reel into three equal parts of 400 feet each, making it possible for her film to work as intended.