Simplify each expression. See Example 1. (-8t^3)(2t^6)(-5t^4)

Question

Accepted Answer

Hey everyone here we are asked to reduce the following expression to the simplest form where we have the quantity of negative are to the fifth power times the quantity of two R to the fourth power times the quantity of negative five are to the sixth power. Now our first step here and simplifying this expression will be to just group together our coefficients and the same variables. So doing this beginning with our coefficients, we have the quantity of negative nine times two times negative five. And now grouping together our our variables, we have the coefficients times the quantity of our to the fifth power times R. To the fourth power times are to the sixth power. So now we just need to continue to simplify this expression and we can do this by first multiplying our coefficient terms together. So doing this, we have negative nine times two times negative five which gives us positive 90. So we have 90 times the quantity of ar to the fifth power times R. To the fourth power times are to the sixth power. So now our next step is to judge, simplify our our variable here and we can do this by recalling the product rule of exponents which tells us that A to the power of M times A. To the power of M is equivalent to A to the power of M plus N. So here we can see our exponents in our given expression here all have the same base. So so like stated in our formula, we can just add together all of their exponents. So doing this, we have the expression 90 times the quantity of ar to the fifth times R. To the fourth times our to the six. Which from our formula we see is equivalent to R. To the power of five plus four plus six. And now we can just finish simplifying our expression here by simplifying this exponents. So our final expression becomes 90 R. To the power of five plus four plus six, which is just 15. So with this we have fully simplified our given expression and we are left with answer choice D. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Simplify each expression. See Example 1. (-8t^3)(2t^6)(-5t^4)

Key Concepts

Multiplication of Monomials

Properties of Exponents

Sign Rules in Multiplication

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