Question

Need the a answer for this

Answer 1

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)`