The given expression is equivalent to [tex]\frac{p^{7}q}{160}[/tex]
What are indices?
An index is a small number that tells us how many times a term has been multiplied by itself.
The plural of index is indices.
Below is an example of a term written in index form :[tex]4^{3}[/tex]
4 is the base and 3 is the index.
We can read this as ‘4 to the power 3’
Another way of expressing [tex]4^{3}[/tex] is
4 x 4 x 4 = 64
Indices can be positive or negative numbers.
Given expression can be written as [tex]\frac{({4p^{-4}q})^{-2}}{10pq^{-3}}[/tex]
Now to simplify the given fractional expression :[tex]\frac{({4p^{-4}q})^{-2}}{10pq^{-3}}[/tex]
= [tex]\frac{4^{-2}p^{8}q^{-2}}{10pq^{-3}}[/tex] By using the property of exponents is given by:
[tex](a^{m})^{n}=a^{m n}[/tex]
=[tex]\frac{p^{7}q}{10 .16}[/tex] By using the property of exponents given by
[tex]a^{m}a^{n}=a^{m + n}[/tex] and [tex]a^{-m}= \frac{1}{a^{m}}[/tex]
= [tex]\frac{p^{7}q}{160}[/tex]
Learn about indices here :
https://brainly.com/question/27327380
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