In Exercises 1–8, multiply the monomials.

(−3xy²z⁵)(2xy⁷z⁴)

Question

In Exercises 1–8, multiply the monomials.

(−3xy²z⁵)(2xy⁷z⁴)

Accepted Answer

Hello, everyone. We are going to perform multiplication for the given mono meals. What we were given is in parentheses negative nine X squared YZ cubed multiplied by the parentheses. Three X cubed, Y raised to the eighth power Z. Our answer choices are a negative 27. X raise the sixth power, Y raise the ninth power Z raised to the fourth power B negative 27 X raised to the fifth power Y raised to the ninth power Z raised to the fourth power C negative 27 X raised to the fifth power Y raised to the eighth power Z raised to the fourth power D negative 27. X raised the fifth power Y raised the ninth power Z cubed wanna rewrite what we were given. So in parentheses, I have negative nine X squared yz cubed closed parentheses multiplied by the parentheses. Three X cubed Y raised to the eighth power Z closed parentheses. I recall that when I'm multiplying mono meals, I'm gonna multiply my like bases. So I'm gonna multiply my X's together. My Ys and my Zs. I also need to multiply the coefficients together. So my coefficients are negative nine and positive three. And those will multiply to negative 27. Next I have X squared times X cubed. And when I multiply like bases, I add their exponents. So X squared multiplied by X cubed will give me X raised to the fifth power. After that, looking at my Y base in the first parentheses, I have Y and it doesn't show me an exponent, but I recall that when it doesn't show an exponent, the exponent is one. So I have why raise to the first power and why raise to the eighth power? And when I multiply those together, I again add my exponents. So I'll get why raise to the ninth power. Then finally, Z I have Z raised to the third power and Z where they don't show me the exponent. So again, I'm gonna put a one there. So Z cubed multiplied by Z to the first power. Again, I'll keep my Z as the base and add the exponents. Three plus one is four. So when I multiply this, my product is negative 27 X raised to the fifth power, Y raised to the ninth power, Z raise to the fourth power. And that is answer choice B have a nice day.

In Exercises 1–8, multiply the monomials. (−3xy²z⁵)(2xy⁷z⁴)

TextbookSolutions.keyConceptsTitle

Monomials

Multiplication of Monomials

Laws of Exponents

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