Simplify the Expression

Question

(-3x⁴y³) (4x^-2y^-5)

Answer 1

Hi Jessica, with this expression the negative exponents seem confusing, but it is indicating that the term is in the denominator.

 

In the problem (-3x⁴y³) (4x^-2y^-5), x^-2 is in the denominator as x² and y-5 is y⁵ in the denominator making the expression look like this:

 

(-3x4y3) (4x-2y-5)

 

=    -3x⁴y³•4

       ––––––––

          x²y⁵

 

Now you would look for the exponents among the terms and find the difference between them. If the exponent is larger in the numerator, than the difference is written there; likewise if not its in the denominator. Here are the exponents written out so you will see how it works:

 

=   -3x4y3•4
     ––––––––
         x²y⁵

 

=    -3 • x•x•x•x • y•y•y  •4
       –––––––––––––––––––
         x•x  •  y•y•y•y•y

 

=   -3 • x•x•x•x • y•y•y •4
        –––––––––––––––––––
           x•x • y•y•y•y•y

 

=   -3 • x•x  •4
     ––––––––––
           y•y

 

=     -12x2
       ––––––––––
            y2

 

Thus, your answer is (-12x²)/y²