Unit 5 Lesson 2 Homework Solutions

This is homework 5.2. This is related to our lesson about expressions with exponents. And problems one through four, it asks, write an each expression is a repeated multiplication. And number one, we have a base which is 7, and an exponent, which is three. That means that we're going to use 7 three times as a factor. So the answer would be 7 times 7 times 7. We're using our base, which is 7 three times, which is a repeated multiplication. Number two, we have 9 as a base and threes and exponents. So we're going to use 9, three times as effective. So we get 9. Times 9 times 9. And then being multiply by two to the power of two or our base is two and our exponent is two. So we're going to use two two times as a factor, so two times two. Then we have V to the fourth power, so we have V times V times V times V and finally number four, we have our variable, which is a to the power of four and time is B to the second power. So we're multiplying a four times a times a times a times a and that is being multiplied times B twice, because we have a base of B and an exponent of two, which means we use B twice as a factor one and two. For number 5, they ask it asks, use an exponent to write each repeated multiplication. So now here we count how many times was 6 years this effector that one, two, three, four, 5, so 5 times what you're supposed to factor. So we have our base, which is 6, and our exponent will be 5, because it was used 5 times as factor. Here, number 6, we have our variable, which is N, and it's being used three times to select a factor. So we get N, our exponent is three. Here we have four, and we have a variable T four, so I'm going to use one as a factor, so we keep that as a four with no exponent, but however T is used twice as a factor so we got to put available T and to the second power. Then the number 8, we have our variable D, use three times as a factor, so we have our base D and our exponent three times F F is only used once as a factor, so there is no exponent on F for number 9 ten and 11 cis simplify following the order of operations remember we first solve the powers so we need to solve four to the second power, which would be four times four, and that is 16. So Terry -16 will be 14. Then number ten, we have a parenthesis, and we have also powers, but we're going to first solve what's in the parentheses. And we do 6 plus two that equals 8, and that's being divided by two to the second power, so that's two times two. And that will be 8 divided by four. And 8 divided by four equals two two. A number 11, we got three to the third power. It's been divided by 9 and added by three. First we solved the powers and three to the third power B three times three times three, and I'll be 27. It's been divided by 9 and added three, and then that's 27 divided by 9. Equals three plus three 6. And number 12, 13 and 14, we need to evaluate when a equals two and B equals 5. So if equals two that's 6 times two to the third power, so two to the third power will be two times two times two, W 8 so 6 times 8 equals 48, then we have B to the second power, so when B equals 5, there will be 5 to the second power times a, which equals two plus three. We saw what's in the parentheses and leaves those with 5. The second power times two plus three is 5. 5 to the second file will be 25. Times 5 equals 125. Then we have B plus a inside the parenthesis to the second power. So first, we'll replace the value of B, which is 5, and we're going to add a value of a, which is two. And 5 plus two is 7. So 7 to the second power equals the 7 times 7, which will be 49. Then exercise is 15 and 16. We need to match the terms of the expression to the parts of the figure. And here we have a square which is a base of three and a height of three, so this square represents this term. And I have a smaller square, which is two times two, and represents this term. Remember that three times three equals two three squared and two times two equals two squared. Now here we have the large square, which is a one, two, three, four, 5 is a base and one, two, three, four, 5, so our height. So that's 5 times 5, which equals 5 squared. So the whole big squared of that represents this term. And smaller square with empty dots represents this term, because we have one, two, and one, two. So that's two times two equals two to the second power. And finally, our question number 17 says Reilly said that four to the 5th power equals 5. What is the mistake that did Riley make? And what is for the 5th power mean? So what Riley did is that he multiply the base times the exponent. Which is one of our most common mistakes. What 5 to the 5th power means repeated multiplication, which is four times four times four times four times four. Multiplying four, our factor four, 5 times.