Question #73eb1

2 Answers
Oct 24, 2017

See below.

Explanation:

To make things easier, you need to know that:

a^(-n)= 1/a^n

Using this and starting with the numerator:

1/4^3 xx 3^4 xx4^2

4^3= 4xx4xx4=64

3^4= 3xx3xx3xx3= 81

4^2= 4xx4=16

So our numerator is now:

1/64xx81xx16=1296/64=20.25

Our denominator is:

3^5xx1/4^2

3^5= 3xx3xx3xx3xx3=243

4^2=16color(white(*) (from above)

So we have:

243/16=15.1875 for the denominator.

Put together:

20.25/15.1875= 1 1/3

Oct 24, 2017

The answer can be found by expanding and cancelling.

Explanation:

Some things to keep in mind are:

  1. an exponent means the number multiplied by itself, for example 4^3 = 4*4*4,
  2. a negative exponent is the inverse of the number multiplied by itself: 4^-3 = 1/4*1/4*1/4
  3. any number divided by itself is one: 3/3=1.

Using this we can first expand the numerator (here I am assuming the question is asking (4^-3 * 3^4 * 4^2) /( 3^5 * 4^-2) rather than 4^-3 * 3^4 * 4^2/3^5 * 4^-2)
4^-3 * 3^4 * 4^2 expands to:
1/4*1/4*1/4*3*3*3*3*4*4
or
(3*3*3*3*4*4)/(4*4*4)

Knowing that any number divided by itself = 1, this becomes
(3*3*3*3*cancel(4)*cancel(4))/(4*cancel(4)*cancel(4))
or
3^4*4^-1

We can see that with the 4's, multiplying 4^2 * 4^-3 gave us 4^-1, showing that we can find the result by adding the exponents! Likewise, dividing by an exponent is the same as subtracting, because 1/3^5 is the same as 3^-5.

so:
(4^-3 * 3^4 * 4^2) /( 3^5 * 4^-2)

=(3^4*4^-1)/( 3^5 * 4^-2)

=3^4*4^-1* 3^-5 * 4^2

=3^4* 3^-5*4^-1*4^2

=3^-1*4^1

=4^1/3^1

=4/3