Simplify each expression. See Example 1. (5x^2y)(-3x^3y^4)

Question

Accepted Answer

Hey everyone here we are asked to reduce the following expression to its simplest form. And we are given the expression where we have the quantity of five A cubed times B times the quantity of negative seven A to the fifth power times B to the eighth power. Now our first step here in simplifying this expression is going to be to collect the coefficients together and also the same variables together. So doing this beginning with our coefficients here we have the quantity of five times negative seven. And now collecting our A terms, we have times the quantity of a cubed times A to the fifth power. Then for our B terms we have finally times the quantity of B times B to the eighth power. So with this we just need to start simplifying our expression here. And we can begin by multiplying our coefficient terms together. So doing this we have five times three which gives us the expression negative 35 times the quantity of a. To the power of three times a. To the power of five times the quantity of B times B to the power of eight. So now we need to start simplifying our variables 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 N is equivalent to A. To the power of M plus N. So again from this formula we see that when we multiply term of the same base or sorry multiply exponents of the same base. We can just add their exponents together. So now with this information we can just simplify our expression here. So we have negative 35 times the quantity of a cubed times A. To the fifth power. Which we see simplifies to just A. To the power of three plus five. And now we multiply by our B terms. So we had B times B to the eighth power. So we really have to be to the power of one plus eight. And now our last step appears to just simplify our exponents. So our final expression becomes negative 35 times A. To the power of three plus five which is just eight times B. To the power of one plus eight which is just nine. And with this we have found our fully simplified expression and we are left with answer choice. C. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Simplify each expression. See Example 1. (5x^2y)(-3x^3y^4)

Key Concepts

Multiplication of Monomials

Exponent Rules

Combining Like Terms

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