We are given expression: [tex]\frac{28p^9q^{-5}}{12p^{-6}q^7}[/tex].
In order to simplify given expression, let us break it into smaller parts.
[tex]\frac{28}{12} = \frac{7}{3}[/tex]
[tex]\frac{p^9}{p^{-6}} =p^{9-(-6)} = p^{9+6} = p^{15}.[/tex]
[tex]\frac{q^{-5}}{q^7} =\frac{1}{q^{7-(-5)}} = \frac{1}{q^{7+5}} = \frac{1}{q^{12}}[/tex]
Combining all terms together, we get
[tex]\frac{7p^{15}}{3q^{12}} .[/tex]
The expression which is equivalent to [tex]28p^{9} q^{-5} /12p^{-6} q^{7}[/tex] is [tex]7p^{15} /3q^{12}[/tex].
Expression is combination of numbers, symbols, coefficients, fraction, indeterminants, etc. It is mostly not found in equal to form. It shows a defined relationship between variables but we cannot find the exact value of variable.
The given expression is [tex]28p^{9} q^{-5} /12p^{-6} q^{7}[/tex] and we have evaluate the expression.
[tex]28p^{9} q^{-5} /12p^{-6} q^{7}[/tex]=[tex]28p^{9}p^{6} /12 q^{7}q^{5}[/tex]
(We have collected variable having positive power in numerator and denominator)
Now we have to add the powers of p and q because base are same and they are in multiplication.
=[tex]28p^{15} /12q^{12}[/tex]
=7[tex]p^{15}[/tex]/3[tex]q^{12}[/tex]
Hence the equivalent expression of [tex]28p^{9} q^{-5} /12p^{-6} q^{7}[/tex] is [tex]7p^{15} /3q^{12}[/tex].
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