Question

Question #73eb1

Answer 1

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`

Answer 2

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`