Question

What is the product of -8x^2y and -2xy^3 ? Use the law of exponents to find the product. > Show your work.

Answer 1

ok if you have \(a^j\), we call a the base and j the exponent . If we multiply two numbers that have the SAME BASE, raised to any exponent, we ADD the exponents. So for example \[a^ja^k=a^{j+k}\]A numerical example would be\[3^2\cdot 3^4=3^{2+4}=3^6\]

Answer 2

so in this case you have \[-8x^2y\cdot -2xy^3\]So you get \[-8\cdot -2 \cdot x^2\cdot x^1\cdot y^1\cdot y^3\]\[=16x^{2+1}y^{3+1}\]

Answer 3

Thank you @richyw for your help!

Answer 4

no worries!and (of course) you would want to write it as \(16x^3y^4\)

Answer 5

Yes, I did do so.