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Evaluate by using scientific notation and the laws of exponents. Leave your answer in scientific notation.$$(55,000,000,000)(16,000,000)$$...

Question

Evaluate by using scientific notation and the laws of exponents. Leave your answer in scientific notation.$$(55,000,000,000)(16,000,000)$$

Evaluate by using scientific notation and the laws of exponents. Leave your answer in scientific notation. $$ (55,000,000,000)(16,000,000) $$



Answers

Scientific Notation Use scientific notation, the Laws of Exponents, and a calculator to perform the indicated operations. State your answer rounded to the number of significant digits indicated by the given data.
$$
\frac{(0.0000162)(0.01582)}{(594,621,000)(0.0058)}
$$

So for this problem, we're going to be simplifying this expression given to us right here. And we're going to be using our properties of experience. Just simplify this into one up number written in scientific notations. So the first property of exponents that we're going to be using all go ahead and write up in the left says that we have two numbers inside of a parentheses. So say, for instance, M and n razed to some power, eh? We can essentially distribute this exponents each of the numbers within the parentheses, so this will be equal to em to the A power times and to the eighth hour. And we're also going to be using the property of exponents. Says that a number raised to some power. So say, for instance, a to the empower raised again to another power. It's, for instance, the end power well simplified to 80 power of M times. And so with that being said, we can go ahead and use our first property to distribute our exponents in the new writer. So our nine will be distributed to the three with decimal and to the 10 to the negative six power and our 12 in the denominator will be again distributed to each of these two terms. So when we do that, we will get 3.5 for two to the ninth power times 10 to the negative six. Power raised to the ninth Power over 5.5 to the 12th Power times 10 to the fourth Power raised me 12 power. And so with these first numbers, the 3.542 and 5.4545505 we can simply plug them into our calculator to simplify them and our second terms in the numerator and denominator. We're going to have to go ahead and use our second property and multiply those two exponents either. So when we punch in these 1st 2 numbers in her calculator, we are going to get, uh, some number. That is around 87,000. Wait 96 continuing on. And then in our denominator, 5.5 to the 12 power is 25615120665 nine with some decibel. And then when we distribute this nine to the 10 to the negative six power, we get times 10 to the negative 54th power and and the denominator distributing this 12 before we get times 10 to the 48th Power. And so to simplify these 1st 2 terms again, we're just going to go ahead and plug them into our calculator. So when we divide them, we get 2.0 31 89896 And then for our terms with me 10 we are going to have to move our top term into the denominator because of the property of negative exponents s as we essentially take the reciprocal of any number or and said to combine all of our steps into one, we can just move this positive 48 in the denominator into the numerator so we can write times 10 to the negative 54 power times 10 to the negative 48 power again. That's taking the term from our denominator right there. And then finally, we are going to use another property of exponents that says two numbers with the same base when multiplied together, we can simplify them to one term of the same base with their exponents added together so that with that, we can write our answer as 0.318 96 times 10 to the negative. 54 plus negative. 48 is equal to negative. 102. And next we're going to convert this first number into a number that is between zero and 10 so that we can get our answer to be in scientific notation. So we're going to count the number of decimals that we have to move, uh, number of places with to move our decibel to the right in order to end up with our decibel right there between the three and the one. So we'll start, you're in count. 1231234 spaces to the right. So this is equal to 3.189 six times 10 to the negative for times 10 to the negative 102 And again we will add these two exponents, which will give us just the 10 part alone. Well, give us 10 to the negative 106 power and our first number. We know that we need to write with the correct number of significant figures. So when dividing, we are going to go ahead and use the number of significant figures as the ah, the least number of significant figures in our initial problem. So our new Raydor has 1234312349 figures and our denominator has 12123 significant figures. So that means that our answer will need to have three significant figures. So we're going to go ahead and round 222 decimal places. So we're going to get three point. Our eight will round up to a nine. So 3.19 times 10 to the negative, 106 power.

So to simplify this expression first, let's convert all of these individual numbers into scientific notation. So we'll begin with 0.162 So to convert, it will move the decimal point over one to three or five times. So this becomes 1.62 Since we went to the right, it's times 10 to the negative fifth power. Then we'll do the same thing for this number. So we'll move the decimal point over two starts to the right. So we get 1.5 82 times 10 to the negative, too. On then in the denominator, when there's a decimal point here, we just can't see it. Still moving over 123 456 78 times. So we get five 0.9462 one times 10 and this is to the positive eighth power. Since this is a large number and then this number, we move over 123 times to get 5.8 times 10 to the negative three. So now, since multiplication is associative, two times is here. We get to rewrite this to put all the decimals together and all the powers of 10 together. So we have 1.62 times, 1.582 over 5.946 to 1 times 5.8. And this is all times. Turn the negative, Beth times 10 to the negative, too. Over 10 to the eighth times, 10 to the negative three. So then we can use a decimal for this or a calculator to find the first expression involving decimals. And then we'll use rules of exponents to simplify the second part. So then, using a calculator, we get 0.743 and then here we use our rules of exponents to combine the tens in the numerator and the tens and the did not a leader. So we have 10 to the negative seventh over 10 50 incidents attracting this would equal turn to the negative 12 the 0.743 times 10 to the negative 12 power. So it's not yet in scientific notation as we need to move the decimal point over on this 0.743 So we move it over to places and so we get 7.43 Since we moved it over to to the right. Our experiment on the negative 10 goes down by two to be it negative 14. And so then going back to the start, we see that looking at significant digits, we always go with the least number. So this one only had to significant dish. It's so we should round this down to have to as well. It's a step in point floor times 10 to the negative. 14th Power is our final can't say.

We have 0.607 We need to write it in a stand in scientific notation. Now we can rewrite it as 607 divided by then please to power six. Now we can relate it as 607 upon 100 multiplied with 100 divided by attend this to power six So it becomes six 0.7 multiplied with tenders to power to multiplied pretend this power minus six So it becomes 6.7 were deployed with tennis father minus four. Now this is a scientific notation off 0.607

Given somebody's 1,250,000. And this question we have to find the scientific notation of the given number. So if our is in scientific notation so it can be represented as articles to a multiple part and the people and here and it's an interior And the true value of a left and 10. Okay. Then it goes to but so they're giving them back in Britain as And .25 And declared where 10 days. About six Here, the true value of which one he calls to go. And you see that inquired scientific notation of that, you remember?


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