Simplify each expression. See Example 1. (35m^4n)(-2/7mn^2)

Question

Accepted Answer

Hey, everyone here, we are asked to reduce the following expression to its simplest form. And we have the expression of the quantity of 25 P squared times Q times the quantity of negative 3/5 times P times Q to the fourth power. So now our first step here in simplifying this expression is going to be to first group together our coefficients here. And then we need to group together the like variables. So doing this beginning with our coefficient terms, we have the quantity of 25 times negative 3/5. And now for our P terms, we have times the quantity of P squared times P. And lastly for our Q variables, we have times the quantity of Q times Q to the fourth power. So now we just need to continue to simplify this expression here. And we can start by multiplying together our coefficient terms. So we have 25 times negative 3/5 which just gives us negative 15. So we have negative 15 times the quantity of P squared times P times the quantity of Q times Q to the fourth power. So now we need to simplify 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 now with this formula, we see that when we multiply terms of the same base, we can just add together their exponents. So with this in mind, we can rewrite our express here. So we have negative 15. And now originally we had P squared times P to the first power, which really is just equivalent to P to the power of two plus one. And now we multiply our Q terms. So we have times the quantity of A Q to the first power times Q to the fourth power, which really just simplifies to Q to the power of one plus four. So now we just have to finish simplifying our exponents here and we see our final expression becomes negative 15 times P to the power of two plus one, which is just three times Q to the power of one plus four, which is just five. So with this, we have fully simplified our original expression here and we are left with answer choice B thanks for watching. I hope you found this video helpful and I'll see you again next time.

Simplify each expression. See Example 1. (35m^4n)(-2/7mn^2)

Key Concepts

Multiplication of Monomials

Simplifying Fractions

Combining Like Terms

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