What is #8x^3 * 7x^2#?

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Answer 1 · 2016-01-13T09:57:24

#56x^5#

To multiply the terms #8x^3# and #7x^2#, you need to multiply the numbers and the #x# terms separately:

# 8x^3 * 7x^2 = (8 * 7) * (x^3 * x^2)#

Now, first of all,

#8 * 7 = 56#.

To compute the product #x^3 * x^2#, you can either use the power rule #x^m * x^n = x^(m+n)#, or think about what those terms actually mean:

#x^3 = x * x * x#
#x^2 = x * x #

Thus,

#x^3 * x^2 = (x * x * x) * (x * x) = x * x * x * x * x = x^5#

In total, you get

# 8x^3 * 7x^2 = (8 * 7) * (x^3 * x^2) = 56 * x^5 = 56x^5#