Question

Need the a answer for this

Answer 1

Answer:

Given expression:

$\dfrac{14a^4b^6c^{-10}}{8a^{-2}b^3c^{-5}}$

Separate the variables:

$\implies \dfrac{14}{8} \cdot \dfrac{a^4}{a^{-2}} \cdot \dfrac{b^6}{b^3} \cdot \dfrac{c^{-10}}{c^{-5}}$

Reduce the first fraction:

$\implies \dfrac{7}{4} \cdot \dfrac{a^4}{a^{-2}} \cdot \dfrac{b^6}{b^3} \cdot \dfrac{c^{-10}}{c^{-5}}$

$\textsf{Apply Division Property of Exponents rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:$

$\implies \dfrac{7}{4} \cdot a^{4-(-2)} \cdot b^{6-3} \cdot c^{-10-(-5)}$

$\implies \dfrac{7}{4} \cdot a^{6} \cdot b^{3} \cdot c^{-5}$

$\textsf{Apply Negative Property of Exponents rule} \quad a^{-n}=\dfrac{1}{a^n}$

$\implies \dfrac{7}{4} \cdot a^{6} \cdot b^{3} \cdot \dfrac{1}{c^5}$

Therefore:

$\implies \dfrac{7a^6b^3}{4c^5}$