Question

Which expression is equivalent to -Assume

Answer 1

Remember
(abc)/(def)=(a/d)/(b/e)(c/f)
and
(x^m)/(x^n)=x^(m-n)
and
x^-m=1/(x^m)
group like terms
(28/12)(p^9/p^-6)(q^-5/q^7)=
(7/3)(p^15)(q^-12)=
$\frac{7p^{15}}{q^{12}}$

Answer 2

The expression is :

$\frac{7}{3}p^{15}q^{-12}$

Further explanation

In general, we are dealing with numbers that can have large or small numbers  

This rank number was originally used as a multiple product

Rank numbers are usually used in scientific notation. Scientific notation is used to express very large/small numbers

Rank notation is used to write the product of repeated numbers in simple form.

Rank form functions to simplify writing and mention of a number that has the same multiplication factors

Traits of Rank Number Operations

1. Multiplication

2. division

3. rank of rank

4. addition

5. reduction

Rank numbers can be

• 1. positive integers

• 2. zero integers

• 3. negative integers

General properties of numbers:

• 1. aᵇ x aⁿ = aᵇ⁺ⁿ

• 2. aᵇ: aⁿ = aᵇ⁻ⁿ, a≠0

• 3. a⁻ᵇ = 1/aᵇ, a≠0

• 4. (aᵇ)ⁿ= aᵇⁿ

• 5. $(\frac{a}{b})^n~=~(\frac{a^n}{b^n})$, b≠0

• and :  

aⁿ : rank number

If we look the task :

$\frac{28p^9q^{-5}}{12p^{-6}q^7}$,  

p ≠0,q≠0

The solution :

$\frac{28}{12}\times~ \frac{p^9}{p^{-6}}\times~\frac{q^{-5}}{q^7}$

$\frac{7}{3}p^{15}q^{-12}$

Learn more

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Keywords : scientific notation, integer, rank number, integer