Question

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

Answer 1

Answer:

The simplified form of n to the -6th power times p to the 3 power is $\frac{p^3}{n^6}$.

Step-by-step 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 $n^{-6}\times p^3$

Using property of exponent $a^{-n}=(\frac{1}{a} )^n$ , we get,

$n^{-6}\times p^3$ as $(\frac{1}{n} )^6\times p^3$

Simplifying, we get,

$\frac{p^3}{n^6}$

Thus, the simplified form of n to the -6th power times p to the 3 power is $\frac{p^3}{n^6}$.

Answer 2

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