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Write each expression using exponents.$$(3 t)(3 t)(-3 t)$$...

Question

Write each expression using exponents.$$(3 t)(3 t)(-3 t)$$

Write each expression using exponents. $$(3 t)(3 t)(-3 t)$$



Answers

Write the expression as a single power of the base. $$ t \cdot\left(t^{3}\right) $$

And this problem, we're being asked to simplify the expression the quantity of two T raised to the fourth power times three to the third power. So I'm gonna first deal with my prime facie, and I'm gonna raise both to and t to the fourth power. So I'm gonna redirect us as two to the fourth times t to the fourth. I'm gonna bring down my three to the third. Now I'm going to raze everything to their respective exploded. So first we're gonna do to to the four power, which means two times, two times, two times two, which is 60. Next, we're gonna raise t to the fourth Power will remember. It has an imaginary explainable one, and now we just need to multiply these explode. It's well, one times four is equal before, so we have 16 t to the fore, and then we have to multiply that by three to the third, which means three times three times three, which is 27. So, lastly, we just need to multiply 16 t to the fourth times 27. So when we multiply 16 by 27 we get 432 and we bring down the T to the fourth power. So our final answer is 400

So to write this in exponential notation that we just count the number of times Ah, that three t is being shown. So that's being well supplied. So 12345 So you can write this as three t to the power of five, and you have to make sure to keep it in parentheses because the exponents has to go to both the coefficient in the variable or if you're simplifying the coefficient. Um, then this is three to the power of five times T to the power bi and three to the power of five is 243. So you can also write this as 243 t to the fifth power.

All right. So here we have, um, a statement, and we need to rewrite an exponential mutation. There are actually several different ways that you can think about this. However, I'm gonna try and tell you the easiest way to do it. So, as you can see, I have three times Teoh times three times sees times you should live and so on. And so on. I have 12345 six off my three teas. So I am going to put three t in parentheses because both three anti are being repeated and multiplied the same number of times. So putting this imprint this season raising it that exponents means that everything inside these parentheses are being repeated and multiplied. So I have again, I have six of them that air here. So I have three times t I put those in parentheses and raise it to the sixth power. So the Easter Ari equivalent expressions. However, this is not. This means that you have three times t times, team times, t times, t times, t times t I. So, by putting it in parentheses, you're telling me and everyone else that that exponents applies to both the three and the tea because this and this are not equal. They were not the same thing. I only have 13 here, and I have six up here. So by putting it in parentheses, I'm seeing that both the three and the TR being raised to the six power written this way. You're just saying that whatever isn't directly in front of that six is what is being released to that sixth powers. So when you write it like this, you're just saying that that T is being raised to the six power when you put it in parentheses. You're saying that both of those things are being raised to the six power?

In this case, there are 123456 seventies So multiplying seventies together you would get t to the seventh power.


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