Simplify each expression. See Example 1.

(-4x⁵) (4x²)

Question

Simplify each expression. See Example 1.

(-4x⁵) (4x²)

Accepted Answer

Welcome back. I am so glad you're here. We're asked for the following polynomial expression to simplify our expression is negative nine M raised to the seventh power multiplied by nine M cubed. Our answer choices are answer choice. A negative 81 M raised to the 21st answer choice B negative 81 M raised to the 10th answer choice C negative nine M raised to the 42nd and answer choice D negative nine M raised to the 10th. All right. So looking at our expression here for these coefficients, this negative nine and the nine, those numbers are being multiplied by each other and we just multiply them as normal. So we take negative nine multiplied by nine, which is negative 81. Now, for these M to the seventh being multiplied by M cubed. We recall from previous lessons that when we have variables with the same base. So if we had a raised to the X multiplied by a, raised to the Y. When we multiply them, we're going to keep that same base. It's still going to be A and we're going to add the exponents. So it will be a raised to the X plus Y. And so here with the M raised to the seventh, multiplied by M raised to the third. We'll keep the M and we will add their exponents together. So seven plus three is a positive 10. So we've got for our simplified expression, negative 81 M raised to the 10th power. We look at our answer choices and this matches with answer choice. B well done. We'll catch you on the next one.

Simplify each expression. See Example 1. (-4x⁵) (4x²)

Key Concepts

Multiplication of Monomials

Exponent Rules

Combining Like Terms

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