Answer:
Given expression:
[tex]\dfrac{14a^4b^6c^{-10}}{8a^{-2}b^3c^{-5}}[/tex]
Separate the variables:
[tex]\implies \dfrac{14}{8} \cdot \dfrac{a^4}{a^{-2}} \cdot \dfrac{b^6}{b^3} \cdot \dfrac{c^{-10}}{c^{-5}}[/tex]
Reduce the first fraction:
[tex]\implies \dfrac{7}{4} \cdot \dfrac{a^4}{a^{-2}} \cdot \dfrac{b^6}{b^3} \cdot \dfrac{c^{-10}}{c^{-5}}[/tex]
[tex]\textsf{Apply Division Property of Exponents rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies \dfrac{7}{4} \cdot a^{4-(-2)} \cdot b^{6-3} \cdot c^{-10-(-5)}[/tex]
[tex]\implies \dfrac{7}{4} \cdot a^{6} \cdot b^{3} \cdot c^{-5}[/tex]
[tex]\textsf{Apply Negative Property of Exponents rule} \quad a^{-n}=\dfrac{1}{a^n}[/tex]
[tex]\implies \dfrac{7}{4} \cdot a^{6} \cdot b^{3} \cdot \dfrac{1}{c^5}[/tex]
Therefore:
[tex]\implies \dfrac{7a^6b^3}{4c^5}[/tex]
