How do you simplify #(7x^-4 y^5) (2x^-3 y^-4)#?

1 Answer
Apr 4, 2017

Answer:

See the entire simplification process below:

Explanation:

First, rewrite the expression as:

#(7 xx 2)(x^-4 * x^-3)(y^5 * y^-4) = 14(x^-4 * x^-3)(y^5 * y^-4)#

Next, use this rule of exponents to multiply the variables:

#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#14(x^color(red)(-4) * x^color(blue)(-3))(y^color(red)(5) * y^color(blue)(-4)) = 14x^(color(red)(-4) + color(blue)(-3))y^(color(red)(5) + color(blue)(-4)) = 14x^-7y^1#

Then, use this rule of exponents to complete the simplification for the #y# variable:

#a^color(red)(1) = a#

#14x^-7y^color(red)(1) = 14x^-7y#

Now, use this rule of exponents to complete the simplification:

#x^color(red)(a) = 1/x^color(red)(-a)#

#14x^color(red)(-7)y = (14y)/x^color(red)(- -7) = (14y)/x^7#