Need the a answer for this

Question 1

Question 2

Answer:

Given expression:

(14a^4b^6c^(-10))/(8a^(-2)b^3c^(-5))

Separate the variables:

$\implies (14)/(8) \cdot (a^4)/(a^(-2)) \cdot (b^6)/(b^3) \cdot (c^(-10))/(c^(-5))$

Reduce the first fraction:

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

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

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

$\implies (7)/(4) \cdot a^(6) \cdot b^(3) \cdot c^(-5)$

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

$\implies (7)/(4) \cdot a^(6) \cdot b^(3) \cdot (1)/(c^5)$

Therefore:

$\implies (7a^6b^3)/(4c^5)$

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