What is #(8a^3b^2)(2a^-4b^-5)#?

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Answer 1 · 2016-12-24T13:31:03

#16a^-1b^-3#

First, combine the terms within parenthesis:

#(color(red)(8a^3b^2))(color(blue)(2a^-4b^-5)) -> color(red)(8a^3b^2)color(blue)(2a^-4b^-5)#

Now we can group like terms by rearranging the terms:

#color(red)(8) * color(blue)(2) * color(red)(a^3) * color(blue)(a^-4) * color(red)(b^2) * color(blue)(b^-5)#

We can now use the rule of exponents which states:

#color(green)(x^a * x^b = x^(a+b)#

#16 * a^(color(red)(3)color(blue)(-4)) * b^(color(red)(2)color(blue)(-5)) ->#

#16 * a^-1 * b^-3#

#16a^-1b^-3#