How do you simplify \frac { - 18p ^ { - 2} r ^ { 3} h ^ { - 8} v ^ { - 8} } { 9a ^ { - 1} p ^ { 3} r ^ { 3} v ^ { - 2} w }18p2r3h8v89a1p3r3v2w?

2 Answers
Apr 17, 2018

= -(2a)/(p^5h^8v^6w)=2ap5h8v6w

Explanation:

\frac { - 18p ^ { - 2} r ^ { 3} h ^ { - 8} v ^ { - 8} } { 9a ^ { - 1} p ^ { 3} r ^ { 3} v ^ { - 2} w }18p2r3h8v89a1p3r3v2w

First, let's separate the like-terms to make it easier to see what's going on here:

=(-18)/9 * 1/(a^(-1)) * p^-2/p^3 * r^3/r^3 * h^-8/1 * v^-8/v^-2 * 1/w=1891a1p2p3r3r3h81v8v21w

=(-18)/9 * a^0/(a^(-1)) * p^-2/p^3 * r^3/r^3 * h^-8/h^0 * v^-8/v^-2 * w^0/w=189a0a1p2p3r3r3h8h0v8v2w0w

since anything to the 00th power is 11.

The rules for like-terms and powers is:

  • Multiplication of terms requires addition of powers
  • Division of terms requires subtraction of powers

We will need to use the latter.

=-2 * a^(0-(-1)) * p^(-2-3) * r^(3-3) * h^(-8-0) * v^(-8-(-2)) * w^(0-1)=2a0(1)p23r33h80v8(2)w01

=-2 * a^(1) * p^(-5) * r^(0) * h^(-8) * v^(-6) * w^(-1)=2a1p5r0h8v6w1

=-2ap^-5h^-8v^-6w^-1=2ap5h8v6w1

Rewriting with only positive powers (if you would like to):

= -(2a)/(p^5h^8v^6w)=2ap5h8v6w

Apr 17, 2018

-(2a)/(p^5h^8v^6w)2ap5h8v6w or -2ap^-5h^-8v^-6w^-12ap5h8v6w1

Explanation:

first, you can find individual quotients:

18/9 = -2189=2

1/(a^-1) = a^1 = a1a1=a1=a

p^-2/p^2 = p^(-2 - 3) = p^-5p2p2=p23=p5

r^3/r^3 = r^(3-3) = r^0 = 1r3r3=r33=r0=1

h^-8/1 = h^-8h81=h8

v^-8/v^-2 = v^(-8 - -2) = v^(-8 + 2) = v^-6v8v2=v82=v8+2=v6

1/w = w^-11w=w1

multiplying all of these together gives a simplified version of the fraction.

hence, the expression can be written as -2ap^-5h^-8v^-6w^-12ap5h8v6w1.

if you want to have the numerator as only positive exponents, you can write the negative exponents in the previous expression in the denominator.

this gives -(2a)/(p^5h^8v^6w)2ap5h8v6w.