Question

Which is the simplified form of n to the -6th power times p to the 3 power?

Answer 1

The simplified form of n to the -6th power times p to the 3 power is
`(p^3)/(n^6)`.

Explanation:

Given problem: n to the -6th power times p to the 3 power

We have to write the simplified form of given problem.

Consider the given expression n to the -6th power times p to the 3 power.

we can write the expression mathematically as

n to the -6th power can be written as
`n^(-6)`

and p to the 3 power can be written as
`p^(3)`

Combining both, n to the -6th power times p to the 3 power.

written as
`n^(-6)* p^3`

Using property of exponent
`a^(-n)=((1)/(a) )^n` , we get,

`n^(-6)* p^3` as
`((1)/(n) )^6* p^3`

Simplifying, we get,

`(p^3)/(n^6)`

Thus, the simplified form of n to the -6th power times p to the 3 power is
`(p^3)/(n^6)`.

Answer 2

To make a negative exponent become positive we will put it under a 1. So our n to the -6 power becomes
`(1)/(n^6)`. If we multiply that by p to the 3rd, we have
`(1)/(n^6)* (p^3)/(1)` which simplifies to
`(p^3)/(n^6)` and that's as simple as it can get.