Respuesta :

Answer:

The simplified expression is [tex]\frac{12x^8y^5}{5z^4}[/tex]

Therefore [tex]\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}=\frac{12x^8y^5}{5z^4}[/tex]

Step-by-step explanation:

Given expression is [tex]\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}[/tex]

To simplify the given expression as below :

[tex]\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}[/tex]

[tex]=\frac{12x^5y^9z^{-8}}{5x^{-3}y^4z^{-4}}[/tex]

[tex]=\frac{12x^5y^9z^{-8}x^3y^{-4}z^4}{5}[/tex]  ( by using the property [tex]a^{m}=\frac{1}{a^{-m}}[/tex] )

[tex]=\frac{12x^5.x^3.y^9.y^{-4}z^{-8}z^4}{5}[/tex]

[tex]=\frac{12}{5}x^{5+3}.y^{9-4}.z^{-8+4}[/tex] ( by using the property [tex]a^m.a^n=a^{m+n}[/tex] )

[tex]=\frac{12}{5}x^8y^5z^{-4}[/tex]

[tex]=\frac{12x^8y^5}{5z^4}[/tex]  ( by using the property [tex]a^{-m}=\frac{1}{a^m}[/tex] )

[tex]\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}=\frac{12x^8y^5}{5z^4}[/tex]

The simplified expression is [tex]\frac{12x^8y^5}{5z^4}[/tex]

Therefore [tex]\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}=\frac{12x^8y^5}{5z^4}[/tex]

Answer:

Therefore,

[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{12x^{8}y^{5}}{5z^{4}}[/tex]

Step-by-step explanation:

Simplify

[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}[/tex]

Solution:

Using the Identities

[tex]1.\ x^{-a}=\dfrac{1}{x^{a}}[/tex]

[tex]2.\ \dfrac{1}{x^{-a}}=x^{a}[/tex]

[tex]3.\ \dfrac{x^{a}}{x^{b}}=x^{(a-b)}[/tex]

Therefore,

[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{24x^{(5+3)}y^{(9-4)}z^{(-8+4)}}{10}[/tex]

[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{2\times 12x^{8}y^{5}z^{-4}}{2\times 5}[/tex]

[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{12x^{8}y^{5}}{5z^{4}}[/tex]

Therefore,

[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{12x^{8}y^{5}}{5z^{4}}[/tex]

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